diff --git a/python/tests/ibd.py b/python/tests/ibd.py
index db30ead0f8..6db35201b7 100644
--- a/python/tests/ibd.py
+++ b/python/tests/ibd.py
@@ -134,27 +134,69 @@ def __repr__(self):
     def __str__(self):
         return repr(self)
 
-    def add_segment(self, a, b, seg):
+    def add_segment_deprecated(self, a, b, seg):
+        # The original version of add_segment that doesn't sort or squash.
         key = (a, b) if a < b else (b, a)
         self.segments[key].append(tskit.IdentitySegment(seg.left, seg.right, seg.node))
 
-    def sort_and_squash_segments(self, a, b):
-        # Sort and squash in-place. This will work differently in the C implementation.
+    def add_segment(self, a, b, seg):
         key = (a, b) if a < b else (b, a)
-        self.segments[key] = sorted(self.segments[key])
-        num_segs = len(self.segments[key])
-        new_list = []
-        if num_segs > 1:
-            for seg in self.segments[key]:
-                if len(new_list) == 0:
-                    new_list.append(seg)
-                else:
-                    n = new_list[-1]  # last segment
-                    if seg.node != n.node or seg.left != n.right:
-                        new_list.append(seg)
-                    else:
-                        new_list[-1] = tskit.IdentitySegment(n.left, seg.right, n.node)
-            self.segments[key] = new_list
+
+        # Get position and add into the correct position.
+        current_segs = self.segments[key]
+        num_segs = len(current_segs)
+
+        if num_segs == 0:
+            self.segments[key].append(
+                tskit.IdentitySegment(seg.left, seg.right, seg.node)
+            )
+        else:
+            # Find the position for the new segment.
+            i = 0
+            while (
+                i < num_segs
+                and current_segs[i].node <= seg.node
+                and current_segs[i].right <= seg.left
+            ):
+                i += 1
+
+            # Calculate boolean values that determine whether to squash
+            # and if so, where.
+            PUT_FIRST = False  # Insert segment at start of list.
+            PUT_LAST = False  # Insert segment at end of list.
+            SQUASH_LEFT = False  # Squash with the left segment.
+            SQUASH_RIGHT = False  # Squash with the right segment.
+
+            if i == 0:
+                PUT_FIRST = True
+            if i == num_segs:
+                PUT_LAST = True
+            if not PUT_FIRST:
+                if (
+                    current_segs[i - 1].node == seg.node
+                    and current_segs[i - 1].right == seg.left
+                ):
+                    SQUASH_LEFT = True
+            if not PUT_LAST:
+                if (
+                    seg.node == current_segs[i].node
+                    and seg.right == current_segs[i].left
+                ):
+                    SQUASH_RIGHT = True
+
+            # Insert the new segment and squash if needed.
+            if SQUASH_LEFT and not SQUASH_RIGHT:
+                current_segs[i - 1].right = seg.right
+            elif SQUASH_RIGHT and not SQUASH_LEFT:
+                current_segs[i].left = seg.left
+            elif SQUASH_LEFT and SQUASH_RIGHT:
+                # To squash twice, must pop one of the existing segments.
+                current_segs[i - 1].right = current_segs[i].right
+                current_segs.pop(i)
+            else:
+                self.segments[key].insert(
+                    i, tskit.IdentitySegment(seg.left, seg.right, seg.node)
+                )
 
 
 class IbdFinder:
@@ -238,13 +280,18 @@ def record_ibd(self, current_parent, child_segs, squash):
                 # If there are any overlapping segments, record as a new
                 # IBD relationship.
                 if self.passes_filters(seg0.node, seg1.node, left, right):
-                    self.result.add_segment(
-                        seg0.node,
-                        seg1.node,
-                        Segment(left, right, current_parent),
-                    )
                     if squash:
-                        self.result.sort_and_squash_segments(seg0.node, seg1.node)
+                        self.result.add_segment(
+                            seg0.node,
+                            seg1.node,
+                            Segment(left, right, current_parent),
+                        )
+                    else:
+                        self.result.add_segment_deprecated(
+                            seg0.node,
+                            seg1.node,
+                            Segment(left, right, current_parent),
+                        )
                 seg1 = seg1.next
             seg0 = seg0.next