diff --git a/milli/src/search/mod.rs b/milli/src/search/mod.rs
index ca0eda49e..c85b80d2f 100644
--- a/milli/src/search/mod.rs
+++ b/milli/src/search/mod.rs
@@ -276,6 +276,8 @@ pub enum TermsMatchingStrategy {
     Last,
     // all words are mandatory
     All,
+    // remove more frequent word first
+    Frequency,
 }
 
 impl Default for TermsMatchingStrategy {
diff --git a/milli/src/search/new/graph_based_ranking_rule.rs b/milli/src/search/new/graph_based_ranking_rule.rs
index 3136eb190..b066f82bd 100644
--- a/milli/src/search/new/graph_based_ranking_rule.rs
+++ b/milli/src/search/new/graph_based_ranking_rule.rs
@@ -164,6 +164,21 @@ impl<'ctx, G: RankingRuleGraphTrait> RankingRule<'ctx, QueryGraph> for GraphBase
                     }
                     costs
                 }
+                TermsMatchingStrategy::Frequency => {
+                    let removal_order =
+                        query_graph.removal_order_for_terms_matching_strategy_frequency(ctx)?;
+                    let mut forbidden_nodes =
+                        SmallBitmap::for_interned_values_in(&query_graph.nodes);
+                    let mut costs = query_graph.nodes.map(|_| None);
+                    // FIXME: this works because only words uses termsmatchingstrategy at the moment.
+                    for ns in removal_order {
+                        for n in ns.iter() {
+                            *costs.get_mut(n) = Some((1, forbidden_nodes.clone()));
+                        }
+                        forbidden_nodes.union(&ns);
+                    }
+                    costs
+                }
                 TermsMatchingStrategy::All => query_graph.nodes.map(|_| None),
             }
         } else {
diff --git a/milli/src/search/new/mod.rs b/milli/src/search/new/mod.rs
index 5e4c2f829..f178b03cf 100644
--- a/milli/src/search/new/mod.rs
+++ b/milli/src/search/new/mod.rs
@@ -197,6 +197,11 @@ fn resolve_maximally_reduced_query_graph(
             .iter()
             .flat_map(|x| x.iter())
             .collect(),
+        TermsMatchingStrategy::Frequency => query_graph
+            .removal_order_for_terms_matching_strategy_frequency(ctx)?
+            .iter()
+            .flat_map(|x| x.iter())
+            .collect(),
         TermsMatchingStrategy::All => vec![],
     };
     graph.remove_nodes_keep_edges(&nodes_to_remove);
diff --git a/milli/src/search/new/query_graph.rs b/milli/src/search/new/query_graph.rs
index d34d0afb5..9cbe55aff 100644
--- a/milli/src/search/new/query_graph.rs
+++ b/milli/src/search/new/query_graph.rs
@@ -3,6 +3,7 @@ use std::collections::BTreeMap;
 use std::hash::{Hash, Hasher};
 
 use fxhash::{FxHashMap, FxHasher};
+use roaring::RoaringBitmap;
 
 use super::interner::{FixedSizeInterner, Interned};
 use super::query_term::{
@@ -11,6 +12,7 @@ use super::query_term::{
 use super::small_bitmap::SmallBitmap;
 use super::SearchContext;
 use crate::search::new::interner::Interner;
+use crate::search::new::resolve_query_graph::compute_query_term_subset_docids;
 use crate::Result;
 
 /// A node of the [`QueryGraph`].
@@ -290,6 +292,49 @@ impl QueryGraph {
         }
     }
 
+    pub fn removal_order_for_terms_matching_strategy_frequency(
+        &self,
+        ctx: &mut SearchContext,
+    ) -> Result<Vec<SmallBitmap<QueryNode>>> {
+        // lookup frequency for each term
+        let mut term_with_frequency: Vec<(u8, u64)> = {
+            let mut term_docids: BTreeMap<u8, RoaringBitmap> = Default::default();
+            for (_, node) in self.nodes.iter() {
+                match &node.data {
+                    QueryNodeData::Term(t) => {
+                        let docids = compute_query_term_subset_docids(ctx, &t.term_subset)?;
+                        for id in t.term_ids.clone() {
+                            term_docids
+                                .entry(id)
+                                .and_modify(|curr| *curr |= &docids)
+                                .or_insert_with(|| docids.clone());
+                        }
+                    }
+                    QueryNodeData::Deleted | QueryNodeData::Start | QueryNodeData::End => continue,
+                }
+            }
+            term_docids
+                .into_iter()
+                .map(|(idx, docids)| match docids.len() {
+                    0 => (idx, u64::max_value()),
+                    frequency => (idx, frequency),
+                })
+                .collect()
+        };
+        term_with_frequency.sort_by_key(|(_, frequency)| *frequency);
+        let mut term_weight = BTreeMap::new();
+        let mut weight: u16 = 1;
+        let mut peekable = term_with_frequency.into_iter().peekable();
+        while let Some((idx, frequency)) = peekable.next() {
+            term_weight.insert(idx, weight);
+            if peekable.peek().map_or(false, |(_, f)| frequency < *f) {
+                weight += 1;
+            }
+        }
+        let cost_of_term_idx = move |term_idx: u8| *term_weight.get(&term_idx).unwrap();
+        Ok(self.removal_order_for_terms_matching_strategy(ctx, cost_of_term_idx))
+    }
+
     pub fn removal_order_for_terms_matching_strategy_last(
         &self,
         ctx: &SearchContext,
@@ -315,10 +360,19 @@ impl QueryGraph {
         if first_term_idx >= last_term_idx {
             return vec![];
         }
+
         let cost_of_term_idx = |term_idx: u8| {
             let rank = 1 + last_term_idx - term_idx;
             rank as u16
         };
+        self.removal_order_for_terms_matching_strategy(ctx, cost_of_term_idx)
+    }
+
+    pub fn removal_order_for_terms_matching_strategy(
+        &self,
+        ctx: &SearchContext,
+        order: impl Fn(u8) -> u16,
+    ) -> Vec<SmallBitmap<QueryNode>> {
         let mut nodes_to_remove = BTreeMap::<u16, SmallBitmap<QueryNode>>::new();
         let mut at_least_one_mandatory_term = false;
         for (node_id, node) in self.nodes.iter() {
@@ -329,7 +383,7 @@ impl QueryGraph {
             }
             let mut cost = 0;
             for id in t.term_ids.clone() {
-                cost = std::cmp::max(cost, cost_of_term_idx(id));
+                cost = std::cmp::max(cost, order(id));
             }
             nodes_to_remove
                 .entry(cost)
diff --git a/milli/tests/search/mod.rs b/milli/tests/search/mod.rs
index 9193ab762..310780e03 100644
--- a/milli/tests/search/mod.rs
+++ b/milli/tests/search/mod.rs
@@ -159,6 +159,7 @@ pub fn expected_order(
 
     match optional_words {
         TermsMatchingStrategy::Last => groups.into_iter().flatten().collect(),
+        TermsMatchingStrategy::Frequency => groups.into_iter().flatten().collect(),
         TermsMatchingStrategy::All => {
             groups.into_iter().flatten().filter(|d| d.word_rank == 0).collect()
         }