diff --git a/loopy/transform/precompute.py b/loopy/transform/precompute.py
index 7fabaface..906e2ae2a 100644
--- a/loopy/transform/precompute.py
+++ b/loopy/transform/precompute.py
@@ -239,7 +239,7 @@ def __init__(self, rule_mapping_context, subst_name, subst_tag, within,
             access_descriptors, array_base_map,
             storage_axis_names, storage_axis_sources,
             non1_storage_axis_names,
-            temporary_name, compute_insn_id, compute_dep_id,
+            temporary_name, compute_dep_ids,
             compute_read_variables):
         super().__init__(rule_mapping_context)
 
@@ -255,8 +255,7 @@ def __init__(self, rule_mapping_context, subst_name, subst_tag, within,
         self.non1_storage_axis_names = non1_storage_axis_names
 
         self.temporary_name = temporary_name
-        self.compute_insn_id = compute_insn_id
-        self.compute_dep_id = compute_dep_id
+        self.compute_dep_ids = compute_dep_ids
 
         self.compute_read_variables = compute_read_variables
         self.compute_insn_depends_on = set()
@@ -339,7 +338,6 @@ def map_subst_rule(self, name, tag, arguments, expn_state):
     def map_kernel(self, kernel):
         new_insns = []
 
-        excluded_insn_ids = {self.compute_insn_id, self.compute_dep_id}
         # precomputed_in_insns: set of insn ids in which the subst rule was
         # precomputed.
         precomputed_in_insns = set()
@@ -359,20 +357,19 @@ def map_kernel(self, kernel):
             if self.replaced_something:
                 insn = insn.copy(
                         depends_on=(
-                            insn.depends_on
-                            | frozenset([self.compute_dep_id])))
+                            insn.depends_on | self.compute_dep_ids))
 
                 precomputed_in_insns.add(insn.id)
 
                 for dep in insn.depends_on:
-                    if dep in excluded_insn_ids:
+                    if dep in self.compute_dep_ids:
                         continue
 
                     dep_insn = kernel.id_to_insn[dep]
                     if (frozenset(dep_insn.assignee_var_names())
                             & self.compute_read_variables):
                         self.compute_insn_depends_on.update(
-                                insn.depends_on - excluded_insn_ids)
+                                insn.depends_on - self.compute_dep_ids)
 
             new_insns.append(insn)
 
@@ -967,7 +964,7 @@ def add_assumptions(d):
             expression=compute_expression,
             # within_inames determined below
             )
-    compute_dep_id = compute_insn_id
+    compute_dep_ids = {compute_insn_id}
     added_compute_insns: list[InstructionBase] = [compute_insn]
 
     if temporary_address_space == AddressSpace.GLOBAL:
@@ -979,7 +976,7 @@ def add_assumptions(d):
                 depends_on=frozenset([compute_insn_id]),
                 synchronization_kind="global",
                 mem_kind="global")
-        compute_dep_id = barrier_insn_id
+        compute_dep_ids.add(barrier_insn_id)
 
         added_compute_insns.append(barrier_insn)
 
@@ -995,7 +992,7 @@ def add_assumptions(d):
             access_descriptors, abm,
             storage_axis_names, storage_axis_sources,
             non1_storage_axis_names,
-            temporary_name, compute_insn_id, compute_dep_id,
+            temporary_name, frozenset(compute_dep_ids),
             compute_read_variables=get_dependencies(expander(compute_expression)))
 
     kernel = invr.map_kernel(kernel)