diff --git a/test/image-prepare b/test/image-prepare
index 931497684edc..7669231af2fa 100755
--- a/test/image-prepare
+++ b/test/image-prepare
@@ -34,7 +34,7 @@ TEST_DIR = f'{BASE_DIR}/test'
 BOTS_DIR = f'{BASE_DIR}/bots'
 
 
-def build_rpms(dist_tar, image, verbose, quick):
+def build_rpms(dist_tar, image, verbose, quick, *, disable_pybridge=False):
     """build RPMs from a tarball in an image
 
     Return local rpm path list.
@@ -54,9 +54,10 @@ def build_rpms(dist_tar, image, verbose, quick):
 
         # build rpms
         mock_opts = ("--verbose" if verbose else "") + (" --nocheck" if quick else "")
+        defines = '--define "cockpit_enable_python 0"' if disable_pybridge else ""
         machine.execute(fr"""
             su builder -c 'mock --no-clean --disablerepo=* --offline \
-                                --resultdir /var/tmp/build {mock_opts} \
+                                --resultdir /var/tmp/build {mock_opts} {defines} \
                                 --rebuild /var/tmp/build/SRPMS/*.src.rpm'
         """, timeout=1800)
 
@@ -124,7 +125,9 @@ def build_install_ostree(dist_tar, image, verbose, quick):
     OSTree image can't build packages, build them on corresponding OSes and invoke
     test/ostree.install to install them into the OSTree and the cockpit/ws container.
     """
-    rpms = build_rpms(dist_tar, testmap.get_build_image(image), verbose, quick)
+    # fedora-coreos and rhel4edge not yet ready for pybridge
+    rpms = build_rpms(dist_tar, testmap.get_build_image(image), verbose, quick,
+                      disable_pybridge=image in ["fedora-coreos", "rhel4edge"])
     args = []
     for rpm in rpms:
         args += ["--upload", f"{rpm}:/var/tmp/"]
diff --git a/test/verify/check-client b/test/verify/check-client
index d4b1eb001432..d0c9c1f490c4 100755
--- a/test/verify/check-client
+++ b/test/verify/check-client
@@ -20,8 +20,8 @@
 import testlib
 
 
-# Run this on more OSes as we roll out the pybridge
-@testlib.onlyImage("needs pybridge", "debian-testing", "ubuntu-stable")
+@testlib.skipImage("needs pybridge", "debian-stable", "ubuntu-2204", "fedora-37", "fedora-coreos",
+                   "rhel-8*", "centos-8*", "rhel-9*", "centos-9*", "rhel4edge")
 class TestClient(testlib.MachineCase):
 
     provision = {
diff --git a/tools/cockpit.spec b/tools/cockpit.spec
index 4a611179e99c..63c7df2c5a4d 100644
--- a/tools/cockpit.spec
+++ b/tools/cockpit.spec
@@ -53,10 +53,11 @@ Version:        0
 Release:        1%{?dist}
 Source0:        https://github.com/cockpit-project/cockpit/releases/download/%{version}/cockpit-%{version}.tar.xz
 
-# Use Python bridge on non-stable versions
-%if 0%{?fedora} >= 39
+%if !%{defined cockpit_enable_python}
+%if 0%{?fedora} >= 38
 %define cockpit_enable_python 1
 %endif
+%endif
 
 %if !%{defined cockpit_enable_python}
 %define cockpit_enable_python 0