diff --git a/src/collector/sort_key/order.rs b/src/collector/sort_key/order.rs
index 923d5cb8e..5e7b80669 100644
--- a/src/collector/sort_key/order.rs
+++ b/src/collector/sort_key/order.rs
@@ -322,11 +322,12 @@ impl<TSegmentSortKeyComputer, TSegmentSortKey, TComparator> SegmentSortKeyComput
     for SegmentSortKeyComputerWithComparator<TSegmentSortKeyComputer, TComparator>
 where
     TSegmentSortKeyComputer: SegmentSortKeyComputer<SegmentSortKey = TSegmentSortKey>,
-    TSegmentSortKey: PartialOrd + Clone + 'static + Sync + Send,
+    TSegmentSortKey: Clone + 'static + Sync + Send,
     TComparator: Comparator<TSegmentSortKey> + 'static + Sync + Send,
 {
     type SortKey = TSegmentSortKeyComputer::SortKey;
     type SegmentSortKey = TSegmentSortKey;
+    type SegmentComparator = TComparator;
 
     fn segment_sort_key(&mut self, doc: DocId, score: Score) -> Self::SegmentSortKey {
         self.segment_sort_key_computer.segment_sort_key(doc, score)
diff --git a/src/collector/sort_key/sort_by_score.rs b/src/collector/sort_key/sort_by_score.rs
index df8b0dd75..a23660e56 100644
--- a/src/collector/sort_key/sort_by_score.rs
+++ b/src/collector/sort_key/sort_by_score.rs
@@ -63,8 +63,8 @@ impl SortKeyComputer for SortBySimilarityScore {
 
 impl SegmentSortKeyComputer for SortBySimilarityScore {
     type SortKey = Score;
-
     type SegmentSortKey = Score;
+    type SegmentComparator = NaturalComparator;
 
     #[inline(always)]
     fn segment_sort_key(&mut self, _doc: DocId, score: Score) -> Score {
diff --git a/src/collector/sort_key/sort_by_static_fast_value.rs b/src/collector/sort_key/sort_by_static_fast_value.rs
index b38b8b034..44a4e1d8d 100644
--- a/src/collector/sort_key/sort_by_static_fast_value.rs
+++ b/src/collector/sort_key/sort_by_static_fast_value.rs
@@ -34,9 +34,7 @@ impl<T: FastValue> SortByStaticFastValue<T> {
 
 impl<T: FastValue> SortKeyComputer for SortByStaticFastValue<T> {
     type Child = SortByFastValueSegmentSortKeyComputer<T>;
-
     type SortKey = Option<T>;
-
     type Comparator = NaturalComparator;
 
     fn check_schema(&self, schema: &crate::schema::Schema) -> crate::Result<()> {
@@ -84,8 +82,8 @@ pub struct SortByFastValueSegmentSortKeyComputer<T> {
 
 impl<T: FastValue> SegmentSortKeyComputer for SortByFastValueSegmentSortKeyComputer<T> {
     type SortKey = Option<T>;
-
     type SegmentSortKey = Option<u64>;
+    type SegmentComparator = NaturalComparator;
 
     #[inline(always)]
     fn segment_sort_key(&mut self, doc: DocId, _score: Score) -> Self::SegmentSortKey {
diff --git a/src/collector/sort_key/sort_by_string.rs b/src/collector/sort_key/sort_by_string.rs
index 41ef22e9b..c7f449619 100644
--- a/src/collector/sort_key/sort_by_string.rs
+++ b/src/collector/sort_key/sort_by_string.rs
@@ -30,9 +30,7 @@ impl SortByString {
 
 impl SortKeyComputer for SortByString {
     type SortKey = Option<String>;
-
     type Child = ByStringColumnSegmentSortKeyComputer;
-
     type Comparator = NaturalComparator;
 
     fn segment_sort_key_computer(
@@ -50,8 +48,8 @@ pub struct ByStringColumnSegmentSortKeyComputer {
 
 impl SegmentSortKeyComputer for ByStringColumnSegmentSortKeyComputer {
     type SortKey = Option<String>;
-
     type SegmentSortKey = Option<TermOrdinal>;
+    type SegmentComparator = NaturalComparator;
 
     #[inline(always)]
     fn segment_sort_key(&mut self, doc: DocId, _score: Score) -> Option<TermOrdinal> {
diff --git a/src/collector/sort_key/sort_key_computer.rs b/src/collector/sort_key/sort_key_computer.rs
index d56fa7cd0..ccfe44e05 100644
--- a/src/collector/sort_key/sort_key_computer.rs
+++ b/src/collector/sort_key/sort_key_computer.rs
@@ -12,13 +12,21 @@ use crate::{DocAddress, DocId, Result, Score, SegmentReader};
 /// It is the segment local version of the [`SortKeyComputer`].
 pub trait SegmentSortKeyComputer: 'static {
     /// The final score being emitted.
-    type SortKey: 'static + PartialOrd + Send + Sync + Clone;
+    type SortKey: 'static + Send + Sync + Clone;
 
     /// Sort key used by at the segment level by the `SegmentSortKeyComputer`.
     ///
     /// It is typically small like a `u64`, and is meant to be converted
     /// to the final score at the end of the collection of the segment.
-    type SegmentSortKey: 'static + PartialOrd + Clone + Send + Sync + Clone;
+    type SegmentSortKey: 'static + Clone + Send + Sync + Clone;
+
+    /// Comparator type.
+    type SegmentComparator: Comparator<Self::SegmentSortKey> + 'static;
+
+    /// Returns the segment sort key comparator.
+    fn segment_comparator(&self) -> Self::SegmentComparator {
+        Self::SegmentComparator::default()
+    }
 
     /// Computes the sort key for the given document and score.
     fn segment_sort_key(&mut self, doc: DocId, score: Score) -> Self::SegmentSortKey;
@@ -47,7 +55,7 @@ pub trait SegmentSortKeyComputer: 'static {
         left: &Self::SegmentSortKey,
         right: &Self::SegmentSortKey,
     ) -> Ordering {
-        NaturalComparator.compare(left, right)
+        self.segment_comparator().compare(left, right)
     }
 
     /// Implementing this method makes it possible to avoid computing
@@ -81,7 +89,7 @@ pub trait SegmentSortKeyComputer: 'static {
 /// the sort key at a segment scale.
 pub trait SortKeyComputer: Sync {
     /// The sort key type.
-    type SortKey: 'static + Send + Sync + PartialOrd + Clone + std::fmt::Debug;
+    type SortKey: 'static + Send + Sync + Clone + std::fmt::Debug;
     /// Type of the associated [`SegmentSortKeyComputer`].
     type Child: SegmentSortKeyComputer<SortKey = Self::SortKey>;
     /// Comparator type.
@@ -188,6 +196,11 @@ where
         TailSegmentSortKeyComputer::SegmentSortKey,
     );
 
+    type SegmentComparator = (
+        HeadSegmentSortKeyComputer::SegmentComparator,
+        TailSegmentSortKeyComputer::SegmentComparator,
+    );
+
     /// A SegmentSortKeyComputer maps to a SegmentSortKey, but it can also decide on
     /// its ordering.
     ///
@@ -269,11 +282,12 @@ impl<T, PreviousScore, NewScore> SegmentSortKeyComputer
     for MappedSegmentSortKeyComputer<T, PreviousScore, NewScore>
 where
     T: SegmentSortKeyComputer<SortKey = PreviousScore>,
-    PreviousScore: 'static + Clone + Send + Sync + PartialOrd,
-    NewScore: 'static + Clone + Send + Sync + PartialOrd,
+    PreviousScore: 'static + Clone + Send + Sync,
+    NewScore: 'static + Clone + Send + Sync,
 {
     type SortKey = NewScore;
     type SegmentSortKey = T::SegmentSortKey;
+    type SegmentComparator = T::SegmentComparator;
 
     fn segment_sort_key(&mut self, doc: DocId, score: Score) -> Self::SegmentSortKey {
         self.sort_key_computer.segment_sort_key(doc, score)
@@ -463,6 +477,7 @@ where
 {
     type SortKey = TSortKey;
     type SegmentSortKey = TSortKey;
+    type SegmentComparator = NaturalComparator;
 
     fn segment_sort_key(&mut self, doc: DocId, _score: Score) -> TSortKey {
         (self)(doc)
diff --git a/src/collector/top_score_collector.rs b/src/collector/top_score_collector.rs
index 78c344dbe..631169bc0 100644
--- a/src/collector/top_score_collector.rs
+++ b/src/collector/top_score_collector.rs
@@ -325,7 +325,7 @@ impl TopDocs {
         sort_key_computer: impl SortKeyComputer<SortKey = TSortKey> + Send + 'static,
     ) -> impl Collector<Fruit = Vec<(TSortKey, DocAddress)>>
     where
-        TSortKey: 'static + Clone + Send + Sync + PartialOrd + std::fmt::Debug,
+        TSortKey: 'static + Clone + Send + Sync + std::fmt::Debug,
     {
         TopBySortKeyCollector::new(sort_key_computer, self.doc_range())
     }
@@ -446,7 +446,7 @@ where
     F: 'static + Send + Sync + Fn(&SegmentReader) -> TTweakScoreSortKeyFn,
     TTweakScoreSortKeyFn: 'static + Fn(DocId, Score) -> TSortKey,
     TweakScoreSegmentSortKeyComputer<TTweakScoreSortKeyFn>:
-        SegmentSortKeyComputer<SortKey = TSortKey>,
+        SegmentSortKeyComputer<SortKey = TSortKey, SegmentSortKey = TSortKey>,
     TSortKey: 'static + PartialOrd + Clone + Send + Sync + std::fmt::Debug,
 {
     type SortKey = TSortKey;
@@ -481,6 +481,7 @@ where
 {
     type SortKey = TSortKey;
     type SegmentSortKey = TSortKey;
+    type SegmentComparator = NaturalComparator;
 
     fn segment_sort_key(&mut self, doc: DocId, score: Score) -> TSortKey {
         (self.sort_key_fn)(doc, score)