diff --git a/kindred_solver/solver.py b/kindred_solver/solver.py
index 8de9f1d..3d8e76a 100644
--- a/kindred_solver/solver.py
+++ b/kindred_solver/solver.py
@@ -538,6 +538,16 @@ def _build_constraint(
 
     if kind == kcsolve.BaseJointKind.DistancePointPoint:
         distance = c_params[0] if c_params else 0.0
+        if distance == 0.0:
+            # Distance=0 is point coincidence.  Use CoincidentConstraint
+            # (3 linear residuals) instead of the squared form which has
+            # a degenerate Jacobian when the constraint is satisfied.
+            return CoincidentConstraint(
+                body_i,
+                marker_i_pos,
+                body_j,
+                marker_j_pos,
+            )
         return DistancePointPointConstraint(
             body_i,
             marker_i_pos,