diff --git a/MEMO b/MEMO
index 19e54706ddaf37dd845abd595dcee519df7c3280..1866105afda277641eeda021374196fd56416d0c 100644
--- a/MEMO
+++ b/MEMO
@@ -39,6 +39,16 @@ Things to consider
 To-do
 ^^^^^
 
+- dim_max caching
+
+- Pick not just axis 0, but all axes by lowest available stride
+
+- Unidirectional unification
+
+- Unification Wildcards
+
+- No looking at the lead domain?
+
 - Fix all tests
 
 - Deal with equality constraints.
diff --git a/loopy/__init__.py b/loopy/__init__.py
index a66b9958f6efc1b9491e2e6d13308ffe34e2ac1f..7fd63dff33fc9693956f6255908bb2684f0ab765 100644
--- a/loopy/__init__.py
+++ b/loopy/__init__.py
@@ -382,17 +382,22 @@ def tag_dimensions(kernel, iname_to_tag, force=False):
     iname_to_tag = dict((iname, parse_tag(tag))
             for iname, tag in iname_to_tag.iteritems())
 
-    from loopy.kernel import ParallelTag
+    from loopy.kernel import (ParallelTag, AutoLocalIndexTagBase,
+            LocalIndexTag)
 
     new_iname_to_tag = kernel.iname_to_tag.copy()
     for iname, new_tag in iname_to_tag.iteritems():
         old_tag = kernel.iname_to_tag.get(iname)
 
-        if old_tag is not None and new_tag is None:
-            raise ValueError("cannot untag iname '%s'" % iname)
+        retag_ok = False
+
+        if (isinstance(old_tag, AutoLocalIndexTagBase)
+                and (new_tag is None
+                    or isinstance(new_tag, LocalIndexTag))):
+            retag_ok = True
 
-        if new_tag is None:
-            continue
+        if not retag_ok and old_tag is not None and new_tag is None:
+            raise ValueError("cannot untag iname '%s'" % iname)
 
         if iname not in kernel.all_inames():
             raise ValueError("cannot tag '%s'--not known" % iname)
@@ -401,7 +406,7 @@ def tag_dimensions(kernel, iname_to_tag, force=False):
             raise ValueError("cannot tag '%s' as parallel--"
                     "iname requires sequential execution" % iname)
 
-        if (not force) and old_tag is not None and (old_tag != new_tag):
+        if (not retag_ok) and (not force) and old_tag is not None and (old_tag != new_tag):
             raise RuntimeError("'%s' is already tagged '%s'--cannot retag"
                     % (iname, old_tag))