diff --git a/loopy/preprocess.py b/loopy/preprocess.py
index 0b19ff416b2ca15e9d626a1644b9223367da2f69..3e8c70e536e6852cea5f603cda5265a676062237 100644
--- a/loopy/preprocess.py
+++ b/loopy/preprocess.py
@@ -1946,13 +1946,13 @@ def realize_reduction(kernel, insn_id_filter=None, unknown_types_ok=True,
 def realize_ilp(kernel):
     logger.debug("%s: add axes to temporaries for ilp" % kernel.name)
 
-    from loopy.kernel.data import IlpBaseTag, VectorizeTag
+    from loopy.kernel.data import (IlpBaseTag, VectorizeTag,
+                                   filter_iname_tags_by_type)
 
-    privatizing_inames = frozenset(iname
-            for iname in kernel.all_inames()
-            if isinstance(
-                kernel.iname_to_tag.get(iname),
-                (IlpBaseTag, VectorizeTag)))
+    privatizing_inames = frozenset(
+        iname for iname, tags in six.iteritems(kernel.iname_to_tags)
+        if filter_iname_tags_by_type(tags, (IlpBaseTag, VectorizeTag))
+    )
 
     from loopy.transform.privatize import privatize_temporaries_with_inames
     return privatize_temporaries_with_inames(kernel, privatizing_inames)
diff --git a/loopy/transform/precompute.py b/loopy/transform/precompute.py
index 4755ca1774a15480a2c6b255380dd724e47f9042..1af16f92f8f18b4c08742b0059267350b6904835 100644
--- a/loopy/transform/precompute.py
+++ b/loopy/transform/precompute.py
@@ -993,12 +993,9 @@ def precompute(kernel, subst_use, sweep_inames=[], within=None,
     from loopy import tag_inames
     kernel = tag_inames(kernel, new_iname_to_tag)
 
-    from loopy.kernel.data import AutoFitLocalIndexTag
-    has_automatic_axes = any(
-            isinstance(tag, AutoFitLocalIndexTag)
-            for tag in new_iname_to_tag.values())
+    from loopy.kernel.data import AutoFitLocalIndexTag, filter_iname_tags_by_type
 
-    if has_automatic_axes:
+    if filter_iname_tags_by_type(new_iname_to_tag.values(), AutoFitLocalIndexTag):
         from loopy.kernel.tools import assign_automatic_axes
         kernel = assign_automatic_axes(kernel)