diff --git a/loopy/kernel/instruction.py b/loopy/kernel/instruction.py
index 921d2538a5068a8c309fe9f412aba588aa6243f2..c54d1fc329a3a8797b17458dc40e489044e9374a 100644
--- a/loopy/kernel/instruction.py
+++ b/loopy/kernel/instruction.py
@@ -364,7 +364,7 @@ class InstructionBase(Record):
             raise RuntimeError("unexpected value for Instruction.boostable")
 
         if self.depends_on:
-            result.append("deps="+":".join(self.depends_on))
+            result.append("dep="+":".join(self.depends_on))
         if self.no_sync_with:
             result.append("nosync="+":".join(self.no_sync_with))
         if self.groups:
diff --git a/loopy/transform/precompute.py b/loopy/transform/precompute.py
index 27fad67f8838622d24e276defc7b8c66eaf11306..db993b771d9088f0644c2406704f5b2e4c97ea89 100644
--- a/loopy/transform/precompute.py
+++ b/loopy/transform/precompute.py
@@ -136,7 +136,7 @@ class RuleInvocationReplacer(RuleAwareIdentityMapper):
             access_descriptors, array_base_map,
             storage_axis_names, storage_axis_sources,
             non1_storage_axis_names,
-            temporary_name, compute_insn_id):
+            temporary_name, compute_insn_id, compute_read_variables):
         super(RuleInvocationReplacer, self).__init__(rule_mapping_context)
 
         self.subst_name = subst_name
@@ -153,6 +153,9 @@ class RuleInvocationReplacer(RuleAwareIdentityMapper):
         self.temporary_name = temporary_name
         self.compute_insn_id = compute_insn_id
 
+        self.compute_read_variables = compute_read_variables
+        self.compute_insn_deps = set()
+
     def map_substitution(self, name, tag, arguments, expn_state):
         if not (
                 name == self.subst_name
@@ -230,6 +233,16 @@ class RuleInvocationReplacer(RuleAwareIdentityMapper):
                             insn.depends_on
                             | frozenset([self.compute_insn_id])))
 
+                for dep in insn.depends_on:
+                    if dep == self.compute_insn_id:
+                        continue
+
+                    dep_insn = kernel.id_to_insn[dep]
+                    if (frozenset(dep_insn.assignee_var_names())
+                            & self.compute_read_variables):
+                        self.compute_insn_deps.update(
+                                insn.depends_on - set([self.compute_insn_id]))
+
             new_insns.append(insn)
 
         return kernel.copy(instructions=new_insns)
@@ -782,12 +795,16 @@ def precompute(kernel, subst_use, sweep_inames=[], within=None,
 
     # {{{ substitute rule into expressions in kernel (if within footprint)
 
+    from loopy.symbolic import SubstitutionRuleExpander
+    expander = SubstitutionRuleExpander(kernel.substitutions)
+
     invr = RuleInvocationReplacer(rule_mapping_context,
             subst_name, subst_tag, within,
             access_descriptors, abm,
             storage_axis_names, storage_axis_sources,
             non1_storage_axis_names,
-            temporary_name, compute_insn_id)
+            temporary_name, compute_insn_id,
+            compute_read_variables=get_dependencies(expander(compute_expression)))
 
     kernel = invr.map_kernel(kernel)
     kernel = kernel.copy(
@@ -796,6 +813,17 @@ def precompute(kernel, subst_use, sweep_inames=[], within=None,
 
     # }}}
 
+    # {{{ add dependencies to compute insn
+
+    kernel = kernel.copy(
+            instructions=[
+                insn.copy(depends_on=frozenset(invr.compute_insn_deps))
+                if insn.id == compute_insn_id
+                else insn
+                for insn in kernel.instructions])
+
+    # }}}
+
     # {{{ determine inames for compute insn
 
     if precompute_outer_inames is None: