diff --git a/loopy/kernel/tools.py b/loopy/kernel/tools.py
index 5a100d7120892e6cfef80e4ee1cd1f1d6cd3bc5b..9ae3e18b93f1a855c28827926cfd1b42f5fc5f9f 100644
--- a/loopy/kernel/tools.py
+++ b/loopy/kernel/tools.py
@@ -135,15 +135,15 @@ def find_all_insn_inames(kernel):
     insn_id_to_inames = {}
     insn_assignee_inames = {}
 
-    all_read_deps = {}
-    all_write_deps = {}
-
     from loopy.transform.subst import expand_subst
     kernel = expand_subst(kernel)
 
+    from loopy.preprocess import add_default_dependencies
+    kernel = add_default_dependencies(kernel)
+
     for insn in kernel.instructions:
-        all_read_deps[insn.id] = read_deps = insn.read_dependency_names()
-        all_write_deps[insn.id] = write_deps = insn.write_dependency_names()
+        read_deps = insn.read_dependency_names()
+        write_deps = insn.write_dependency_names()
         deps = read_deps | write_deps
 
         if insn.forced_iname_deps_is_final:
@@ -168,8 +168,6 @@ def find_all_insn_inames(kernel):
                 write_deps & kernel.all_inames()
                 | insn.stop_iname_dep_propagation)
 
-    written_vars = kernel.get_written_variables()
-
     # fixed point iteration until all iname dep sets have converged
 
     # Why is fixed point iteration necessary here? Consider the following
@@ -196,35 +194,38 @@ def find_all_insn_inames(kernel):
             # of iname deps of all writers, and add those to insn's
             # dependencies.
 
-            for tv_name in (all_read_deps[insn.id] & written_vars):
-                implicit_inames = None
+            implicit_inames = None
+            inames_old_start = inames_old = insn_id_to_inames[insn.id]
 
-                for writer_id in writer_map[tv_name]:
-                    writer_implicit_inames = (
-                            insn_id_to_inames[writer_id]
-                            - insn_assignee_inames[writer_id])
-                    if implicit_inames is None:
-                        implicit_inames = writer_implicit_inames
-                    else:
-                        implicit_inames = (implicit_inames
-                                & writer_implicit_inames)
+            for dep_id in insn.depends_on:
+                writer_implicit_inames = (
+                        insn_id_to_inames[dep_id]
+                        - insn_assignee_inames[dep_id])
+                if implicit_inames is None:
+                    implicit_inames = writer_implicit_inames
+                else:
+                    implicit_inames = (implicit_inames
+                            & writer_implicit_inames)
 
-                inames_old = insn_id_to_inames[insn.id]
+            if implicit_inames is not None:
                 inames_new = (inames_old | implicit_inames) \
                             - insn.reduction_inames()
-                insn_id_to_inames[insn.id] = inames_new
+            else:
+                inames_new = inames_old
+
+            insn_id_to_inames[insn.id] = inames_new
 
-                if inames_new != inames_old:
-                    did_something = True
-                    logger.debug("%s: find_all_insn_inames: %s -> %s (dep-based)" % (
-                        kernel.name, insn.id, ", ".join(sorted(inames_new))))
+            if inames_new != inames_old:
+                did_something = True
+                logger.debug("%s: find_all_insn_inames: %s -> %s (dep-based)" % (
+                    kernel.name, insn.id, ", ".join(sorted(inames_new))))
 
             # }}}
 
             # {{{ domain-based propagation
 
             inames_old = insn_id_to_inames[insn.id]
-            inames_new = set(insn_id_to_inames[insn.id])
+            inames_new = set(inames_old)
 
             for iname in inames_old:
                 home_domain = kernel.domains[kernel.get_home_domain_index(iname)]
@@ -242,10 +243,14 @@ def find_all_insn_inames(kernel):
 
                     if par in kernel.temporary_variables:
                         for writer_id in writer_map.get(par, []):
-                            inames_new.update(insn_id_to_inames[writer_id])
+                            inames_new.update(
+                                    insn_id_to_inames[writer_id]
+                                    - insn.reduction_inames())
 
             if inames_new != inames_old:
                 did_something = True
+                assert inames_new != inames_old_start
+
                 insn_id_to_inames[insn.id] = frozenset(inames_new)
                 logger.debug("%s: find_all_insn_inames: %s -> %s (domain-based)" % (
                     kernel.name, insn.id, ", ".join(sorted(inames_new))))
diff --git a/test/test_linalg.py b/test/test_linalg.py
index e3cae8557a2266bb7b27adb4d6148ed2cda32063..a28d885c1af4c8f595bf65274a8f794ec5d34bdd 100644
--- a/test/test_linalg.py
+++ b/test/test_linalg.py
@@ -628,6 +628,23 @@ def test_small_batched_matvec(ctx_factory):
             parameters=dict(K=K))
 
 
+def test_outer_product(ctx_factory):
+    logging.basicConfig(level=logging.DEBUG)
+    #ctx = ctx_factory()
+
+    knl = lp.make_kernel(
+            "{[i,j]: 0<=i,j<n}}",
+            """
+            z = a[i]*b[j]  {id=init_z}
+            z = z*2        {id=mult_z,dep=init_z}
+            c[i,j] = z     {dep=mult_z}
+            """)
+
+    print(knl)
+
+    assert knl.insn_inames("mult_z") == frozenset(["i", "j"])
+
+
 if __name__ == "__main__":
     if len(sys.argv) > 1:
         exec(sys.argv[1])