diff --git a/milli/src/search/criteria/asc_desc.rs b/milli/src/search/criteria/asc_desc.rs
index a492096d7..378e1c8da 100644
--- a/milli/src/search/criteria/asc_desc.rs
+++ b/milli/src/search/criteria/asc_desc.rs
@@ -198,7 +198,7 @@ fn facet_ordered_iterative<'t>(
 }
 
 fn facet_extreme_value<'t>(
-    mut extreme_it: Box<dyn Iterator<Item = heed::Result<(RoaringBitmap, &[u8])>> + 't>,
+    mut extreme_it: impl Iterator<Item = heed::Result<(RoaringBitmap, &'t [u8])>> + 't,
 ) -> Result<Option<f64>> {
     let extreme_value =
         if let Some(extreme_value) = extreme_it.next() { extreme_value } else { return Ok(None) };
@@ -236,21 +236,22 @@ fn facet_ordered_set_based<'t>(
     is_ascending: bool,
     candidates: RoaringBitmap,
 ) -> Result<Box<dyn Iterator<Item = heed::Result<RoaringBitmap>> + 't>> {
-    let make_iter = if is_ascending { ascending_facet_sort } else { descending_facet_sort };
+    let number_db =
+        index.facet_id_f64_docids.remap_key_type::<FacetGroupKeyCodec<ByteSliceRefCodec>>();
+    let string_db =
+        index.facet_id_string_docids.remap_key_type::<FacetGroupKeyCodec<ByteSliceRefCodec>>();
 
-    let number_iter = make_iter(
-        rtxn,
-        index.facet_id_f64_docids.remap_key_type::<FacetGroupKeyCodec<ByteSliceRefCodec>>(),
-        field_id,
-        candidates.clone(),
-    )?;
+    let (number_iter, string_iter) = if is_ascending {
+        let number_iter = ascending_facet_sort(rtxn, number_db, field_id, candidates.clone())?;
+        let string_iter = ascending_facet_sort(rtxn, string_db, field_id, candidates)?;
 
-    let string_iter = make_iter(
-        rtxn,
-        index.facet_id_string_docids.remap_key_type::<FacetGroupKeyCodec<ByteSliceRefCodec>>(),
-        field_id,
-        candidates,
-    )?;
+        (itertools::Either::Left(number_iter), itertools::Either::Left(string_iter))
+    } else {
+        let number_iter = descending_facet_sort(rtxn, number_db, field_id, candidates.clone())?;
+        let string_iter = descending_facet_sort(rtxn, string_db, field_id, candidates)?;
+
+        (itertools::Either::Right(number_iter), itertools::Either::Right(string_iter))
+    };
 
     Ok(Box::new(number_iter.chain(string_iter).map(|res| res.map(|(doc_ids, _)| doc_ids))))
 }
diff --git a/milli/src/search/facet/facet_sort_ascending.rs b/milli/src/search/facet/facet_sort_ascending.rs
index b0f1dccd5..f59b884de 100644
--- a/milli/src/search/facet/facet_sort_ascending.rs
+++ b/milli/src/search/facet/facet_sort_ascending.rs
@@ -34,15 +34,20 @@ pub fn ascending_facet_sort<'t>(
     db: heed::Database<FacetGroupKeyCodec<ByteSliceRefCodec>, FacetGroupValueCodec>,
     field_id: u16,
     candidates: RoaringBitmap,
-) -> Result<Box<dyn Iterator<Item = Result<(RoaringBitmap, &'t [u8])>> + 't>> {
+) -> Result<impl Iterator<Item = Result<(RoaringBitmap, &'t [u8])>> + 't> {
     let highest_level = get_highest_level(rtxn, db, field_id)?;
     if let Some(first_bound) = get_first_facet_value::<ByteSliceRefCodec>(rtxn, db, field_id)? {
         let first_key = FacetGroupKey { field_id, level: highest_level, left_bound: first_bound };
         let iter = db.range(rtxn, &(first_key..)).unwrap().take(usize::MAX);
 
-        Ok(Box::new(AscendingFacetSort { rtxn, db, field_id, stack: vec![(candidates, iter)] }))
+        Ok(itertools::Either::Left(AscendingFacetSort {
+            rtxn,
+            db,
+            field_id,
+            stack: vec![(candidates, iter)],
+        }))
     } else {
-        Ok(Box::new(std::iter::empty()))
+        Ok(itertools::Either::Right(std::iter::empty()))
     }
 }
 
diff --git a/milli/src/search/facet/facet_sort_descending.rs b/milli/src/search/facet/facet_sort_descending.rs
index fbcc41b9d..454b12859 100644
--- a/milli/src/search/facet/facet_sort_descending.rs
+++ b/milli/src/search/facet/facet_sort_descending.rs
@@ -17,21 +17,21 @@ pub fn descending_facet_sort<'t>(
     db: heed::Database<FacetGroupKeyCodec<ByteSliceRefCodec>, FacetGroupValueCodec>,
     field_id: u16,
     candidates: RoaringBitmap,
-) -> Result<Box<dyn Iterator<Item = Result<(RoaringBitmap, &'t [u8])>> + 't>> {
+) -> Result<impl Iterator<Item = Result<(RoaringBitmap, &'t [u8])>> + 't> {
     let highest_level = get_highest_level(rtxn, db, field_id)?;
     if let Some(first_bound) = get_first_facet_value::<ByteSliceRefCodec>(rtxn, db, field_id)? {
         let first_key = FacetGroupKey { field_id, level: highest_level, left_bound: first_bound };
         let last_bound = get_last_facet_value::<ByteSliceRefCodec>(rtxn, db, field_id)?.unwrap();
         let last_key = FacetGroupKey { field_id, level: highest_level, left_bound: last_bound };
         let iter = db.rev_range(rtxn, &(first_key..=last_key))?.take(usize::MAX);
-        Ok(Box::new(DescendingFacetSort {
+        Ok(itertools::Either::Left(DescendingFacetSort {
             rtxn,
             db,
             field_id,
             stack: vec![(candidates, iter, Bound::Included(last_bound))],
         }))
     } else {
-        Ok(Box::new(std::iter::empty()))
+        Ok(itertools::Either::Right(std::iter::empty()))
     }
 }