diff --git a/glibc.spec b/glibc.spec
index bf96630..5b0aabd 100644
--- a/glibc.spec
+++ b/glibc.spec
@@ -170,7 +170,7 @@ Version: %{glibcversion}
 # - It allows using the Release number without the %%dist tag in the dependency
 #   generator to make the generated requires interchangeable between Rawhide
 #   and ELN (.elnYY < .fcXX).
-%global baserelease 21
+%global baserelease 22
 Release: %{baserelease}%{?dist}
 
 # Licenses:
@@ -359,6 +359,10 @@ Requires: basesystem
 # after nss_*.x86_64.  (See below for the other ordering.)
 Recommends: (nss_db(x86-32) if nss_db(x86-64))
 Recommends: (nss_hesiod(x86-32) if nss_hesiod(x86-64))
+# Deinstall the glibc32 package if present.  This helps tests that do
+# not run against the compose.
+Conflicts: glibc32 <= %{version}-%{baserelease}
+Obsoletes: glibc32 <= %{version}-%{baserelease}
 %endif
 
 # This is for building auxiliary programs like memusage
@@ -2555,6 +2559,9 @@ update_gconv_modules_cache ()
 %endif
 
 %changelog
+* Sun May 19 2024 Florian Weimer <fweimer@redhat.com> - 2.39.9000-22
+- Add Conflicts:/Obsoletes: for glibc32 to glibc.i686
+
 * Sun May 19 2024 Florian Weimer <fweimer@redhat.com> - 2.39.9000-21
 - Auto-sync with upstream branch master,
   commit 8d7b6b4cb27d4dec1dd5f7960298c1699275f962: