diff --git a/test/run-tests.sh b/test/run-tests.sh
index 7d2e8e547f9d1c7860151f5385214423827ea2c5..c8059024b034223aac1d4e424cacf08282bd200b 100755
--- a/test/run-tests.sh
+++ b/test/run-tests.sh
@@ -411,8 +411,9 @@ valid_upgrade_test_p () {
         # Now its hg repository includes 3.0.2.29, but clisp hasn't released in many years(!)
         # We don't punt on upgrade anymore, so we can go at it!
         #clisp:2.00[0-7]:*|clisp:1.*|clisp:2.0[01]*|clisp:2.2[0-5]:*) : ;;
-        # CMUCL has problems with CLOS upgrade in general.
-        cmucl:*) : ;;
+        # CMUCL has problems with 2.32 and earlier because of
+        # the redefinition of system's superclass component.
+        cmucl:1.*|cmucl:2.[012]*|cmucl:2.3[012]*) : ;;
         # Skip many ECL tests, for various ASDF issues
         ecl*:1.*|ecl*:2.0[01]*|ecl*:2.20:*) : ;;
         # GCL 2.7.0 from late November 2013 is required, with ASDF 3.1.2