diff --git a/iree/turbine/kernel/wave/constraints.py b/iree/turbine/kernel/wave/constraints.py
index b83ee825..6310d2a5 100644
--- a/iree/turbine/kernel/wave/constraints.py
+++ b/iree/turbine/kernel/wave/constraints.py
@@ -14,7 +14,6 @@
 from .._support.dtype import DataType
 from ..lang.global_symbols import *
 
-
 """
 Formatting for different target intrinsics:
     <kind>_<elem-type-C>_<M>x<N>x<K>_<elem-type-A>[_<elem-type-B>]
@@ -498,6 +497,27 @@ def apply(self) -> IndexSequence:
             raise ValueError("Index is being computed without setting wave id")
         return IndexSequence(self.tile_size * self.wave_id, 1)
 
+    def set_wave_id_from_hardware_and_workgroup_constraint(
+        self,
+        hardware_constraint: HardwareConstraint,
+        workgroup_constraint: WorkgroupConstraint,
+    ):
+        """
+        The wave_id is the same as the thread_id, with the exception of
+          wave_id[0] = thread_id[0] / threads_per_wave
+        This is a convention that we adopt.
+        """
+        old_wave_id = self.wave_id
+        assert self.dim == workgroup_constraint.dim, "Dimension mismatch"
+        self.wave_id = hardware_constraint.get_thread_id_from_workgroup_dim(
+            workgroup_constraint.workgroup_dim
+        )
+        if workgroup_constraint.workgroup_dim == 0:
+            self.wave_id = floor(self.wave_id / hardware_constraint.threads_per_wave)
+        assert (
+            old_wave_id is None or self.wave_id == old_wave_id
+        ), f"Conflicting preset wave_id old: {old_wave_id} new: {self.wave_id}"
+
 
 def get_constrained_shape(
     shape: list[IndexExpr], constraints: list[WorkgroupConstraint | TilingConstraint]
diff --git a/iree/turbine/kernel/wave/wave.py b/iree/turbine/kernel/wave/wave.py
index c9bee670..066740ac 100644
--- a/iree/turbine/kernel/wave/wave.py
+++ b/iree/turbine/kernel/wave/wave.py
@@ -209,20 +209,10 @@ def initialize_wave_constraints(self, trace: CapturedTrace) -> None:
         hardware_constraint = self.hardware_constraints[0]
         for wave_constraint in self.wave_constraints:
             for workgroup_constraint in self.workgroup_constraints:
-                # The wave_id is the same as the thread_id, with the exception
-                # of wave_id[0] = thread_id[0] / threads_per_wave. This is
-                # a convention that we adopt.
                 if wave_constraint.dim == workgroup_constraint.dim:
-                    wave_constraint.wave_id = (
-                        hardware_constraint.get_thread_id_from_workgroup_dim(
-                            workgroup_constraint.workgroup_dim
-                        )
+                    wave_constraint.set_wave_id_from_hardware_and_workgroup_constraint(
+                        hardware_constraint, workgroup_constraint
                     )
-                    if workgroup_constraint.workgroup_dim == 0:
-                        wave_constraint.wave_id = sympy.floor(
-                            wave_constraint.wave_id
-                            / hardware_constraint.threads_per_wave
-                        )
 
     def initialize_reductions(self, trace: CapturedTrace) -> None:
         """