diff --git a/Cython.spec b/Cython.spec
index 5baee89..1e900eb 100644
--- a/Cython.spec
+++ b/Cython.spec
@@ -32,13 +32,17 @@ BuildRequires:  python3-setuptools
 %if %{with tests}
 BuildRequires:  gcc-c++
 BuildRequires:  python3-numpy
+%if %{undefined rhel}
 # The tests requiring jedi are optional and skipped when jedi is not installed.
 # Note that the jedi tests were forcefully disabled a long time ago,
 # in https://github.com/cython/cython/issues/1845 far, far away.
 # We keep the dependency here so we don't forget to re-add it once the balance is restored.
 # We don't want to pull in jedi to RHEL just to potentially run more tests.
-%if %{undefined rhel}
 BuildRequires:  python3-jedi
+# The pyximport functionality uses the removed imp module.
+# It has been replaced by importlib in Cython 3.
+# The reference counting regression test uses pyximport, so it is disabled in %%check on RHEL.
+BuildRequires:  (python3-zombie-imp if python3-devel >= 3.12)
 %endif
 %endif
 
@@ -129,7 +133,7 @@ cp -p cython-mode-init.el cython-mode-init.elc %{buildroot}%{_emacs_sitestartdir
 %if %{with tests}
 %check
 # run.pstats_profile_test* fails on Python 3.12
-%{python3} runtests.py -vv --no-pyregr %{?_smp_mflags} \
+%{python3} runtests.py -vv --no-pyregr %{?rhel:--no-refnanny} %{?_smp_mflags} \
   --exclude 'run.pstats_profile_test*' \
   %ifarch %{ix86}
   --exclude run.parallel  # https://github.com/cython/cython/issues/2807