diff --git a/milli/src/external_documents_ids.rs b/milli/src/external_documents_ids.rs
index 3dec638da..3dce18b00 100644
--- a/milli/src/external_documents_ids.rs
+++ b/milli/src/external_documents_ids.rs
@@ -1,8 +1,13 @@
 use std::borrow::Cow;
+use std::collections::HashMap;
 use std::convert::TryInto;
+use std::{fmt, str};
 
+use fst::map::IndexedValue;
 use fst::{IntoStreamer, Streamer};
 
+const DELETED_ID: u64 = u64::MAX;
+
 pub struct ExternalDocumentsIds<'a> {
     pub(crate) hard: fst::Map<Cow<'a, [u8]>>,
     pub(crate) soft: fst::Map<Cow<'a, [u8]>>,
@@ -31,8 +36,7 @@ impl<'a> ExternalDocumentsIds<'a> {
     pub fn get<A: AsRef<[u8]>>(&self, external_id: A) -> Option<u32> {
         let external_id = external_id.as_ref();
         match self.soft.get(external_id).or_else(|| self.hard.get(external_id)) {
-            // u64 MAX means deleted in the soft fst map
-            Some(id) if id != u64::MAX => Some(id.try_into().unwrap()),
+            Some(id) if id != DELETED_ID => Some(id.try_into().unwrap()),
             _otherwise => None,
         }
     }
@@ -47,9 +51,10 @@ impl<'a> ExternalDocumentsIds<'a> {
             if docids.iter().any(|v| v.index == 1) {
                 // If the `other` set returns a value here it means
                 // that it must be marked as deleted.
-                new_soft_builder.insert(external_id, u64::MAX)?;
+                new_soft_builder.insert(external_id, DELETED_ID)?;
             } else {
-                new_soft_builder.insert(external_id, docids[0].value)?;
+                let value = docids.iter().find(|v| v.index == 0).unwrap().value;
+                new_soft_builder.insert(external_id, value)?;
             }
         }
 
@@ -65,8 +70,8 @@ impl<'a> ExternalDocumentsIds<'a> {
 
         let mut new_soft_builder = fst::MapBuilder::memory();
         let mut iter = union_op.into_stream();
-        while let Some((external_id, docids)) = iter.next() {
-            let id = docids.last().unwrap().value;
+        while let Some((external_id, marked_docids)) = iter.next() {
+            let id = indexed_last_value(marked_docids).unwrap();
             new_soft_builder.insert(external_id, id)?;
         }
 
@@ -77,19 +82,34 @@ impl<'a> ExternalDocumentsIds<'a> {
         self.merge_soft_into_hard()
     }
 
+    /// An helper function to debug this type, returns an `HashMap` of both,
+    /// soft and hard fst maps, combined.
+    pub fn to_hash_map(&self) -> HashMap<String, u32> {
+        let mut map = HashMap::new();
+
+        let union_op = self.hard.op().add(&self.soft).r#union();
+        let mut iter = union_op.into_stream();
+        while let Some((external_id, marked_docids)) = iter.next() {
+            let id = indexed_last_value(marked_docids).unwrap();
+            if id != DELETED_ID {
+                let external_id = str::from_utf8(external_id).unwrap();
+                map.insert(external_id.to_owned(), id.try_into().unwrap());
+            }
+        }
+
+        map
+    }
+
     fn merge_soft_into_hard(&mut self) -> fst::Result<()> {
         if self.soft.len() >= self.hard.len() / 2 {
             let union_op = self.hard.op().add(&self.soft).r#union();
 
             let mut iter = union_op.into_stream();
             let mut new_hard_builder = fst::MapBuilder::memory();
-            while let Some((external_id, docids)) = iter.next() {
-                if docids.len() == 2 {
-                    if docids[1].value != u64::MAX {
-                        new_hard_builder.insert(external_id, docids[1].value)?;
-                    }
-                } else {
-                    new_hard_builder.insert(external_id, docids[0].value)?;
+            while let Some((external_id, marked_docids)) = iter.next() {
+                let value = indexed_last_value(marked_docids).unwrap();
+                if value != DELETED_ID {
+                    new_hard_builder.insert(external_id, value)?;
                 }
             }
 
@@ -103,6 +123,12 @@ impl<'a> ExternalDocumentsIds<'a> {
     }
 }
 
+impl fmt::Debug for ExternalDocumentsIds<'_> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        f.debug_tuple("ExternalDocumentsIds").field(&self.to_hash_map()).finish()
+    }
+}
+
 impl Default for ExternalDocumentsIds<'static> {
     fn default() -> Self {
         ExternalDocumentsIds {
@@ -112,6 +138,11 @@ impl Default for ExternalDocumentsIds<'static> {
     }
 }
 
+/// Returns the value of the `IndexedValue` with the highest _index_.
+fn indexed_last_value(indexed_values: &[IndexedValue]) -> Option<u64> {
+    indexed_values.iter().copied().max_by_key(|iv| iv.index).map(|iv| iv.value)
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -162,4 +193,25 @@ mod tests {
         assert_eq!(external_documents_ids.get("g"), Some(7));
         assert_eq!(external_documents_ids.get("h"), Some(8));
     }
+
+    #[test]
+    fn strange_delete_insert_ids() {
+        let mut external_documents_ids = ExternalDocumentsIds::default();
+
+        let new_ids =
+            fst::Map::from_iter(vec![("1", 0), ("123", 1), ("30", 2), ("456", 3)]).unwrap();
+        external_documents_ids.insert_ids(&new_ids).unwrap();
+        assert_eq!(external_documents_ids.get("1"), Some(0));
+        assert_eq!(external_documents_ids.get("123"), Some(1));
+        assert_eq!(external_documents_ids.get("30"), Some(2));
+        assert_eq!(external_documents_ids.get("456"), Some(3));
+
+        let deleted_ids = fst::Set::from_iter(vec!["30"]).unwrap();
+        external_documents_ids.delete_ids(deleted_ids).unwrap();
+        assert_eq!(external_documents_ids.get("30"), None);
+
+        let new_ids = fst::Map::from_iter(vec![("30", 2)]).unwrap();
+        external_documents_ids.insert_ids(&new_ids).unwrap();
+        assert_eq!(external_documents_ids.get("30"), Some(2));
+    }
 }
diff --git a/milli/src/index.rs b/milli/src/index.rs
index c8e5ab089..6bcb0aebd 100644
--- a/milli/src/index.rs
+++ b/milli/src/index.rs
@@ -218,7 +218,7 @@ impl Index {
     }
 
     /// Deletes the primary key of the documents, this can be done to reset indexes settings.
-    pub fn delete_primary_key(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
+    pub(crate) fn delete_primary_key(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
         self.main.delete::<_, Str>(wtxn, main_key::PRIMARY_KEY_KEY)
     }
 
@@ -333,7 +333,7 @@ impl Index {
 
     /// Deletes the displayed fields ids, this will make the engine to display
     /// all the documents attributes in the order of the `FieldsIdsMap`.
-    pub fn delete_displayed_fields(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
+    pub(crate) fn delete_displayed_fields(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
         self.main.delete::<_, Str>(wtxn, main_key::DISPLAYED_FIELDS_KEY)
     }
 
@@ -383,7 +383,7 @@ impl Index {
     }
 
     /// Deletes the searchable fields, when no fields are specified, all fields are indexed.
-    pub fn delete_searchable_fields(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
+    pub(crate) fn delete_searchable_fields(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
         self.main.delete::<_, Str>(wtxn, main_key::SEARCHABLE_FIELDS_KEY)
     }
 
@@ -429,7 +429,7 @@ impl Index {
     }
 
     /// Deletes the filterable fields ids in the database.
-    pub fn delete_filterable_fields(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
+    pub(crate) fn delete_filterable_fields(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
         self.main.delete::<_, Str>(wtxn, main_key::FILTERABLE_FIELDS_KEY)
     }
 
@@ -602,7 +602,7 @@ impl Index {
         self.main.put::<_, Str, SerdeJson<&[Criterion]>>(wtxn, main_key::CRITERIA_KEY, &criteria)
     }
 
-    pub fn delete_criteria(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
+    pub(crate) fn delete_criteria(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
         self.main.delete::<_, Str>(wtxn, main_key::CRITERIA_KEY)
     }
 
@@ -642,7 +642,7 @@ impl Index {
         self.main.put::<_, Str, ByteSlice>(wtxn, main_key::STOP_WORDS_KEY, fst.as_fst().as_bytes())
     }
 
-    pub fn delete_stop_words(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
+    pub(crate) fn delete_stop_words(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
         self.main.delete::<_, Str>(wtxn, main_key::STOP_WORDS_KEY)
     }
 
@@ -663,7 +663,7 @@ impl Index {
         self.main.put::<_, Str, SerdeBincode<_>>(wtxn, main_key::SYNONYMS_KEY, synonyms)
     }
 
-    pub fn delete_synonyms(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
+    pub(crate) fn delete_synonyms(&self, wtxn: &mut RwTxn) -> heed::Result<bool> {
         self.main.delete::<_, Str>(wtxn, main_key::SYNONYMS_KEY)
     }
 
diff --git a/milli/src/search/criteria/mod.rs b/milli/src/search/criteria/mod.rs
index 228d48bd7..2ba3b388f 100644
--- a/milli/src/search/criteria/mod.rs
+++ b/milli/src/search/criteria/mod.rs
@@ -328,7 +328,7 @@ pub fn resolve_query_tree<'t>(
                         candidates = docids;
                         first_loop = false;
                     } else {
-                        candidates.intersect_with(&docids);
+                        candidates &= &docids;
                     }
                 }
                 Ok(candidates)
@@ -358,7 +358,7 @@ pub fn resolve_query_tree<'t>(
                 let mut candidates = RoaringBitmap::new();
                 for op in ops {
                     let docids = resolve_operation(ctx, op, wdcache)?;
-                    candidates.union_with(&docids);
+                    candidates |= docids;
                 }
                 Ok(candidates)
             }
@@ -381,7 +381,7 @@ fn all_word_pair_proximity_docids<T: AsRef<str>, U: AsRef<str>>(
             let current_docids = ctx
                 .word_pair_proximity_docids(left.as_ref(), right.as_ref(), proximity)?
                 .unwrap_or_default();
-            docids.union_with(&current_docids);
+            docids |= current_docids;
         }
     }
     Ok(docids)
@@ -401,7 +401,7 @@ fn query_docids(
                 let mut docids = RoaringBitmap::new();
                 for (word, _typo) in words {
                     let current_docids = ctx.word_docids(&word)?.unwrap_or_default();
-                    docids.union_with(&current_docids);
+                    docids |= current_docids;
                 }
                 Ok(docids)
             } else {
@@ -413,7 +413,7 @@ fn query_docids(
             let mut docids = RoaringBitmap::new();
             for (word, _typo) in words {
                 let current_docids = ctx.word_docids(&word)?.unwrap_or_default();
-                docids.union_with(&current_docids);
+                docids |= current_docids;
             }
             Ok(docids)
         }
@@ -430,7 +430,7 @@ fn query_pair_proximity_docids(
     if proximity >= 8 {
         let mut candidates = query_docids(ctx, left, wdcache)?;
         let right_candidates = query_docids(ctx, right, wdcache)?;
-        candidates.intersect_with(&right_candidates);
+        candidates &= right_candidates;
         return Ok(candidates);
     }
 
@@ -463,7 +463,7 @@ fn query_pair_proximity_docids(
                             proximity,
                         )?
                         .unwrap_or_default();
-                    docids.union_with(&current_docids);
+                    docids |= current_docids;
                 }
                 Ok(docids)
             } else if prefix {
diff --git a/milli/src/search/criteria/proximity.rs b/milli/src/search/criteria/proximity.rs
index 3e8196e93..f884de160 100644
--- a/milli/src/search/criteria/proximity.rs
+++ b/milli/src/search/criteria/proximity.rs
@@ -274,11 +274,11 @@ fn resolve_candidates<'t>(
                         let mut candidates =
                             query_pair_proximity_docids(ctx, lr, rl, pair_p + 1, wdcache)?;
                         if lcandidates.len() < rcandidates.len() {
-                            candidates.intersect_with(lcandidates);
-                            candidates.intersect_with(rcandidates);
+                            candidates &= lcandidates;
+                            candidates &= rcandidates;
                         } else {
-                            candidates.intersect_with(rcandidates);
-                            candidates.intersect_with(lcandidates);
+                            candidates &= rcandidates;
+                            candidates &= lcandidates;
                         }
                         if !candidates.is_empty() {
                             output.push((ll.clone(), rr.clone(), candidates));
@@ -317,7 +317,7 @@ fn resolve_candidates<'t>(
                             for (_, rtail, mut candidates) in
                                 mdfs(ctx, tail, proximity - p, cache, wdcache)?
                             {
-                                candidates.intersect_with(&head_candidates);
+                                candidates &= &head_candidates;
                                 if !candidates.is_empty() {
                                     output.push((lhead.clone(), rtail, candidates));
                                 }
@@ -334,7 +334,7 @@ fn resolve_candidates<'t>(
 
     let mut candidates = RoaringBitmap::new();
     for (_, _, cds) in resolve_operation(ctx, query_tree, proximity, cache, wdcache)? {
-        candidates.union_with(&cds);
+        candidates |= cds;
     }
     Ok(candidates)
 }
diff --git a/milli/src/search/criteria/typo.rs b/milli/src/search/criteria/typo.rs
index f4ae15f0a..97a9b4e4b 100644
--- a/milli/src/search/criteria/typo.rs
+++ b/milli/src/search/criteria/typo.rs
@@ -281,7 +281,7 @@ fn resolve_candidates<'t>(
                 let mut candidates = RoaringBitmap::new();
                 for op in ops {
                     let docids = resolve_operation(ctx, op, number_typos, cache, wdcache)?;
-                    candidates.union_with(&docids);
+                    candidates |= docids;
                 }
                 Ok(candidates)
             }
@@ -329,8 +329,8 @@ fn resolve_candidates<'t>(
                     };
                     if !head_candidates.is_empty() {
                         let tail_candidates = mdfs(ctx, tail, mana - m, cache, wdcache)?;
-                        head_candidates.intersect_with(&tail_candidates);
-                        candidates.union_with(&head_candidates);
+                        head_candidates &= tail_candidates;
+                        candidates |= head_candidates;
                     }
                 }
 
diff --git a/milli/src/search/distinct/facet_distinct.rs b/milli/src/search/distinct/facet_distinct.rs
index 290a7602f..91620da2a 100644
--- a/milli/src/search/distinct/facet_distinct.rs
+++ b/milli/src/search/distinct/facet_distinct.rs
@@ -61,7 +61,7 @@ impl<'a> FacetDistinctIter<'a> {
                     db_name: db_name::FACET_ID_STRING_DOCIDS,
                     key: None,
                 })?;
-            self.excluded.union_with(&facet_docids);
+            self.excluded |= facet_docids;
         }
 
         self.excluded.remove(id);
@@ -79,7 +79,7 @@ impl<'a> FacetDistinctIter<'a> {
                     db_name: db_name::FACET_ID_F64_DOCIDS,
                     key: None,
                 })?;
-            self.excluded.union_with(&facet_docids);
+            self.excluded |= facet_docids;
         }
 
         self.excluded.remove(id);
@@ -92,7 +92,7 @@ impl<'a> FacetDistinctIter<'a> {
     /// handling easier.
     fn next_inner(&mut self) -> Result<Option<DocumentId>> {
         // The first step is to remove all the excluded documents from our candidates
-        self.candidates.difference_with(&self.excluded);
+        self.candidates -= &self.excluded;
 
         let mut candidates_iter = self.candidates.iter().skip(self.iter_offset);
         match candidates_iter.next() {
diff --git a/milli/src/search/facet/facet_distribution.rs b/milli/src/search/facet/facet_distribution.rs
index 71816cf5d..3f55006f2 100644
--- a/milli/src/search/facet/facet_distribution.rs
+++ b/milli/src/search/facet/facet_distribution.rs
@@ -122,7 +122,7 @@ impl<'a> FacetDistribution<'a> {
 
         for result in iter {
             let (value, mut docids) = result?;
-            docids.intersect_with(candidates);
+            docids &= candidates;
             if !docids.is_empty() {
                 distribution.insert(value.to_string(), docids.len());
             }
diff --git a/milli/src/search/facet/filter_condition.rs b/milli/src/search/facet/filter_condition.rs
index 31fc6018c..1b1eafcab 100644
--- a/milli/src/search/facet/filter_condition.rs
+++ b/milli/src/search/facet/filter_condition.rs
@@ -289,7 +289,7 @@ impl FilterCondition {
         for (i, result) in iter.enumerate() {
             let ((_fid, level, l, r), docids) = result?;
             debug!("{:?} to {:?} (level {}) found {} documents", l, r, level, docids.len());
-            output.union_with(&docids);
+            *output |= docids;
             // We save the leftest and rightest bounds we actually found at this level.
             if i == 0 {
                 left_found = Some(l);
diff --git a/milli/src/search/facet/mod.rs b/milli/src/search/facet/mod.rs
index 240d99ccc..4e900bff4 100644
--- a/milli/src/search/facet/mod.rs
+++ b/milli/src/search/facet/mod.rs
@@ -213,10 +213,10 @@ impl<'t> Iterator for FacetIter<'t> {
 
                 match result {
                     Ok(((_fid, level, left, right), mut docids)) => {
-                        docids.intersect_with(&documents_ids);
+                        docids &= &*documents_ids;
                         if !docids.is_empty() {
                             if self.must_reduce {
-                                documents_ids.difference_with(&docids);
+                                *documents_ids -= &docids;
                             }
 
                             if level == 0 {
diff --git a/milli/src/search/mod.rs b/milli/src/search/mod.rs
index 71d200e0c..f40a6aed6 100644
--- a/milli/src/search/mod.rs
+++ b/milli/src/search/mod.rs
@@ -173,7 +173,7 @@ impl<'a> Search<'a> {
 
             let mut candidates = distinct.distinct(candidates, excluded);
 
-            initial_candidates.union_with(&bucket_candidates);
+            initial_candidates |= bucket_candidates;
 
             if offset != 0 {
                 let discarded = candidates.by_ref().take(offset).count();
diff --git a/milli/src/update/available_documents_ids.rs b/milli/src/update/available_documents_ids.rs
index 9e3fce75d..653bc7dd2 100644
--- a/milli/src/update/available_documents_ids.rs
+++ b/milli/src/update/available_documents_ids.rs
@@ -12,7 +12,7 @@ impl AvailableDocumentsIds {
         match docids.max() {
             Some(last_id) => {
                 let mut available = RoaringBitmap::from_iter(0..last_id);
-                available.difference_with(&docids);
+                available -= docids;
 
                 let iter = match last_id.checked_add(1) {
                     Some(id) => id..=u32::max_value(),
diff --git a/milli/src/update/delete_documents.rs b/milli/src/update/delete_documents.rs
index a0c1f48f5..313f8a909 100644
--- a/milli/src/update/delete_documents.rs
+++ b/milli/src/update/delete_documents.rs
@@ -43,7 +43,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
     }
 
     pub fn delete_documents(&mut self, docids: &RoaringBitmap) {
-        self.documents_ids.union_with(docids);
+        self.documents_ids |= docids;
     }
 
     pub fn delete_external_id(&mut self, external_id: &str) -> Option<u32> {
@@ -65,7 +65,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
         // We remove the documents ids that we want to delete
         // from the documents in the database and write them back.
         let current_documents_ids_len = documents_ids.len();
-        documents_ids.difference_with(&self.documents_ids);
+        documents_ids -= &self.documents_ids;
         self.index.put_documents_ids(self.wtxn, &documents_ids)?;
 
         // We can execute a ClearDocuments operation when the number of documents
@@ -194,7 +194,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
             if let Some((key, mut docids)) = iter.next().transpose()? {
                 if key == word.as_ref() {
                     let previous_len = docids.len();
-                    docids.difference_with(&self.documents_ids);
+                    docids -= &self.documents_ids;
                     if docids.is_empty() {
                         // safety: we don't keep references from inside the LMDB database.
                         unsafe { iter.del_current()? };
@@ -245,7 +245,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
             let (prefix, mut docids) = result?;
             let prefix = prefix.to_owned();
             let previous_len = docids.len();
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             if docids.is_empty() {
                 // safety: we don't keep references from inside the LMDB database.
                 unsafe { iter.del_current()? };
@@ -285,7 +285,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
         while let Some(result) = iter.next() {
             let (key, mut docids) = result?;
             let previous_len = docids.len();
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             if docids.is_empty() {
                 // safety: we don't keep references from inside the LMDB database.
                 unsafe { iter.del_current()? };
@@ -306,7 +306,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
         while let Some(result) = iter.next() {
             let (bytes, mut docids) = result?;
             let previous_len = docids.len();
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             if docids.is_empty() {
                 // safety: we don't keep references from inside the LMDB database.
                 unsafe { iter.del_current()? };
@@ -325,7 +325,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
         while let Some(result) = iter.next() {
             let (bytes, mut docids) = result?;
             let previous_len = docids.len();
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             if docids.is_empty() {
                 // safety: we don't keep references from inside the LMDB database.
                 unsafe { iter.del_current()? };
@@ -344,7 +344,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
         while let Some(result) = iter.next() {
             let (bytes, mut docids) = result?;
             let previous_len = docids.len();
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             if docids.is_empty() {
                 // safety: we don't keep references from inside the LMDB database.
                 unsafe { iter.del_current()? };
@@ -361,7 +361,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
         let mut iter = field_id_word_count_docids.iter_mut(self.wtxn)?;
         while let Some((key, mut docids)) = iter.next().transpose()? {
             let previous_len = docids.len();
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             if docids.is_empty() {
                 // safety: we don't keep references from inside the LMDB database.
                 unsafe { iter.del_current()? };
@@ -390,7 +390,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
         for field_id in self.index.faceted_fields_ids(self.wtxn)? {
             // Remove docids from the number faceted documents ids
             let mut docids = self.index.number_faceted_documents_ids(self.wtxn, field_id)?;
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             self.index.put_number_faceted_documents_ids(self.wtxn, field_id, &docids)?;
 
             remove_docids_from_field_id_docid_facet_value(
@@ -403,7 +403,7 @@ impl<'t, 'u, 'i> DeleteDocuments<'t, 'u, 'i> {
 
             // Remove docids from the string faceted documents ids
             let mut docids = self.index.string_faceted_documents_ids(self.wtxn, field_id)?;
-            docids.difference_with(&self.documents_ids);
+            docids -= &self.documents_ids;
             self.index.put_string_faceted_documents_ids(self.wtxn, field_id, &docids)?;
 
             remove_docids_from_field_id_docid_facet_value(
@@ -456,7 +456,7 @@ where
     while let Some(result) = iter.next() {
         let (bytes, mut docids) = result?;
         let previous_len = docids.len();
-        docids.difference_with(to_remove);
+        docids -= to_remove;
         if docids.is_empty() {
             // safety: we don't keep references from inside the LMDB database.
             unsafe { iter.del_current()? };
diff --git a/milli/src/update/facets.rs b/milli/src/update/facets.rs
index 09f962bbc..0e2cad69d 100644
--- a/milli/src/update/facets.rs
+++ b/milli/src/update/facets.rs
@@ -181,7 +181,7 @@ fn compute_facet_number_levels<'t>(
             }
 
             // The right bound is always the bound we run through.
-            group_docids.union_with(&docids);
+            group_docids |= docids;
             right = value;
         }
 
diff --git a/milli/src/update/index_documents/merge_function.rs b/milli/src/update/index_documents/merge_function.rs
index 3d9ffda6a..17283b232 100644
--- a/milli/src/update/index_documents/merge_function.rs
+++ b/milli/src/update/index_documents/merge_function.rs
@@ -61,8 +61,7 @@ pub fn roaring_bitmap_merge(_key: &[u8], values: &[Cow<[u8]>]) -> Result<Vec<u8>
     let mut head = RoaringBitmap::deserialize_from(&head[..])?;
 
     for value in tail {
-        let bitmap = RoaringBitmap::deserialize_from(&value[..])?;
-        head.union_with(&bitmap);
+        head |= RoaringBitmap::deserialize_from(&value[..])?;
     }
 
     let mut vec = Vec::with_capacity(head.serialized_size());
@@ -75,8 +74,7 @@ pub fn cbo_roaring_bitmap_merge(_key: &[u8], values: &[Cow<[u8]>]) -> Result<Vec
     let mut head = CboRoaringBitmapCodec::deserialize_from(&head[..])?;
 
     for value in tail {
-        let bitmap = CboRoaringBitmapCodec::deserialize_from(&value[..])?;
-        head.union_with(&bitmap);
+        head |= CboRoaringBitmapCodec::deserialize_from(&value[..])?;
     }
 
     let mut vec = Vec::new();
diff --git a/milli/src/update/index_documents/mod.rs b/milli/src/update/index_documents/mod.rs
index 7faa27588..3876d5dc1 100644
--- a/milli/src/update/index_documents/mod.rs
+++ b/milli/src/update/index_documents/mod.rs
@@ -608,8 +608,8 @@ impl<'t, 'u, 'i, 'a> IndexDocuments<'t, 'u, 'i, 'a> {
         self.index.put_external_documents_ids(self.wtxn, &external_documents_ids)?;
 
         // We merge the new documents ids with the existing ones.
-        documents_ids.union_with(&new_documents_ids);
-        documents_ids.union_with(&replaced_documents_ids);
+        documents_ids |= new_documents_ids;
+        documents_ids |= replaced_documents_ids;
         self.index.put_documents_ids(self.wtxn, &documents_ids)?;
 
         let mut database_count = 0;
@@ -845,6 +845,7 @@ mod tests {
     use heed::EnvOpenOptions;
 
     use super::*;
+    use crate::update::DeleteDocuments;
 
     #[test]
     fn simple_document_replacement() {
@@ -1303,4 +1304,52 @@ mod tests {
         builder.execute(Cursor::new(documents), |_, _| ()).unwrap();
         wtxn.commit().unwrap();
     }
+
+    #[test]
+    fn delete_documents_then_insert() {
+        let path = tempfile::tempdir().unwrap();
+        let mut options = EnvOpenOptions::new();
+        options.map_size(10 * 1024 * 1024); // 10 MB
+        let index = Index::new(options, &path).unwrap();
+
+        let mut wtxn = index.write_txn().unwrap();
+        let content = &br#"[
+            { "objectId": 123, "title": "Pride and Prejudice", "comment": "A great book" },
+            { "objectId": 456, "title": "Le Petit Prince",     "comment": "A french book" },
+            { "objectId": 1,   "title": "Alice In Wonderland", "comment": "A weird book" },
+            { "objectId": 30,  "title": "Hamlet" }
+        ]"#[..];
+        let mut builder = IndexDocuments::new(&mut wtxn, &index, 0);
+        builder.update_format(UpdateFormat::Json);
+        builder.execute(content, |_, _| ()).unwrap();
+
+        assert_eq!(index.primary_key(&wtxn).unwrap(), Some("objectId"));
+
+        // Delete not all of the documents but some of them.
+        let mut builder = DeleteDocuments::new(&mut wtxn, &index, 1).unwrap();
+        builder.delete_external_id("30");
+        builder.execute().unwrap();
+
+        let external_documents_ids = index.external_documents_ids(&wtxn).unwrap();
+        assert!(external_documents_ids.get("30").is_none());
+
+        let content = &br#"[
+            { "objectId": 30, "title": "Hamlet" }
+        ]"#[..];
+        let mut builder = IndexDocuments::new(&mut wtxn, &index, 0);
+        builder.update_format(UpdateFormat::Json);
+        builder.execute(content, |_, _| ()).unwrap();
+
+        let external_documents_ids = index.external_documents_ids(&wtxn).unwrap();
+        assert!(external_documents_ids.get("30").is_some());
+
+        let content = &br#"[
+            { "objectId": 30, "title": "Hamlet" }
+        ]"#[..];
+        let mut builder = IndexDocuments::new(&mut wtxn, &index, 0);
+        builder.update_format(UpdateFormat::Json);
+        builder.execute(content, |_, _| ()).unwrap();
+
+        wtxn.commit().unwrap();
+    }
 }
diff --git a/milli/src/update/words_level_positions.rs b/milli/src/update/words_level_positions.rs
index d43cd19b8..c656d7105 100644
--- a/milli/src/update/words_level_positions.rs
+++ b/milli/src/update/words_level_positions.rs
@@ -236,7 +236,7 @@ fn compute_positions_levels(
                 }
 
                 // The right bound is always the bound we run through.
-                group_docids.union_with(&docids);
+                group_docids |= docids;
             }
 
             if !group_docids.is_empty() {