diff --git a/python-psutil.changes b/python-psutil.changes
index 2749969..eac9777 100644
--- a/python-psutil.changes
+++ b/python-psutil.changes
@@ -1,3 +1,16 @@
+-------------------------------------------------------------------
+Fri Jan 29 08:19:00 UTC 2021 - Antonio Larrosa <alarrosa@suse.com>
+
+- Do not install tests (and change the way they're run since they
+  were run from %{buildroot})
+
+-------------------------------------------------------------------
+Thu Jan 28 16:25:35 UTC 2021 - Antonio Larrosa <alarrosa@suse.com>
+
+- Add patch to skip tests related to rlimit and zombie processes
+  that fail when building for python2 on i586:
+  * skip_rlimit_tests_on_python2.patch
+
 -------------------------------------------------------------------
 Mon Jan 25 16:03:37 UTC 2021 - Antonio Larrosa <alarrosa@suse.com>
 
diff --git a/python-psutil.spec b/python-psutil.spec
index 63bb4ec..2280f04 100644
--- a/python-psutil.spec
+++ b/python-psutil.spec
@@ -34,6 +34,8 @@ Patch1:         skip-obs.patch
 # PATCH-FIX-UPSTREAM skip_failing_tests.patch gh#giampaolo/psutil#1635 mcepl@suse.com
 # skip tests failing because of incomplete emulation of the environment in osc build
 Patch2:         skip_failing_tests.patch
+# PATCH-FIX-SLE skip_rlimit_tests_on_python2.patch alarrosa@suse.com
+Patch3:         skip_rlimit_tests_on_python2.patch
 BuildRequires:  %{python_module devel}
 BuildRequires:  %{python_module setuptools}
 BuildRequires:  fdupes
@@ -75,6 +77,7 @@ sed -i "1s/#!.*//" psutil/{__init__.py,_compat.py,_psbsd.py,_pslinux.py,_psosx.p
 %{python_expand mkdir -p %{buildroot}%{_docdir}/%{$python_prefix}-psutil
 cp -r scripts %{buildroot}%{_docdir}/%{$python_prefix}-psutil/
 find %{buildroot}%{_docdir}/%{$python_prefix}-psutil/scripts/ -type f -name "*.py" -exec sed -i "s|#!%{_bindir}/env python.*|#!%{__$python}|" {} \;
+rm -rf %{buildroot}%{$python_sitearch}/psutil/tests
 %fdupes %{buildroot}%{_docdir}/%{$python_prefix}-psutil/
 %fdupes %{buildroot}%{$python_sitearch}
 }
@@ -84,9 +87,10 @@ find %{buildroot}%{_docdir}/%{$python_prefix}-psutil/scripts/ -type f -name "*.p
 export LANG=en_US.UTF-8
 export PSUTIL_TESTING=1
 export TRAVIS=1
+march=`python3 -c "import platform ; print(platform.machine())"`
 
 # Note test_fetch_all is a bit flaky, occasionally failing
-%python_expand PYTHONPATH=%{buildroot}%{$python_sitearch} $python -Wa psutil/tests/runner.py
+%python_expand PYTHONPATH=build/lib.linux-${march}-%{$python_version}/ $python -Wa psutil/tests/runner.py
 %endif
 
 %files %{python_files}
diff --git a/skip_rlimit_tests_on_python2.patch b/skip_rlimit_tests_on_python2.patch
new file mode 100644
index 0000000..6e96549
--- /dev/null
+++ b/skip_rlimit_tests_on_python2.patch
@@ -0,0 +1,52 @@
+Index: psutil-5.8.0/psutil/tests/test_process.py
+===================================================================
+--- psutil-5.8.0.orig/psutil/tests/test_process.py
++++ psutil-5.8.0/psutil/tests/test_process.py
+@@ -416,6 +416,7 @@ class TestProcess(PsutilTestCase):
+             p.ionice(init)
+ 
+     @unittest.skipIf(not HAS_RLIMIT, "not supported")
++    @unittest.skipIf(sys.version_info.major == 2, "not supported on python2")
+     def test_rlimit_get(self):
+         import resource
+         p = psutil.Process(os.getpid())
+@@ -439,6 +440,7 @@ class TestProcess(PsutilTestCase):
+                 self.assertGreaterEqual(ret[1], -1)
+ 
+     @unittest.skipIf(not HAS_RLIMIT, "not supported")
++    @unittest.skipIf(sys.version_info.major == 2, "not supported on python2")
+     def test_rlimit_set(self):
+         p = self.spawn_psproc()
+         p.rlimit(psutil.RLIMIT_NOFILE, (5, 5))
+@@ -452,6 +454,7 @@ class TestProcess(PsutilTestCase):
+             p.rlimit(psutil.RLIMIT_NOFILE, (5, 5, 5))
+ 
+     @unittest.skipIf(not HAS_RLIMIT, "not supported")
++    @unittest.skipIf(sys.version_info.major == 2, "not supported on python2")
+     def test_rlimit(self):
+         p = psutil.Process()
+         testfn = self.get_testfn()
+@@ -472,6 +475,7 @@ class TestProcess(PsutilTestCase):
+             self.assertEqual(p.rlimit(psutil.RLIMIT_FSIZE), (soft, hard))
+ 
+     @unittest.skipIf(not HAS_RLIMIT, "not supported")
++    @unittest.skipIf(sys.version_info.major == 2, "not supported on python2")
+     def test_rlimit_infinity(self):
+         # First set a limit, then re-set it by specifying INFINITY
+         # and assume we overridden the previous limit.
+@@ -487,6 +491,7 @@ class TestProcess(PsutilTestCase):
+             self.assertEqual(p.rlimit(psutil.RLIMIT_FSIZE), (soft, hard))
+ 
+     @unittest.skipIf(not HAS_RLIMIT, "not supported")
++    @unittest.skipIf(sys.version_info.major == 2, "not supported on python2")
+     def test_rlimit_infinity_value(self):
+         # RLIMIT_FSIZE should be RLIM_INFINITY, which will be a really
+         # big number on a platform with large file support.  On these
+@@ -1270,6 +1275,7 @@ class TestProcess(PsutilTestCase):
+             self.assertEqual(normcase(p.exe()), normcase(PYTHON_EXE))
+ 
+     @unittest.skipIf(not POSIX, 'POSIX only')
++    @unittest.skipIf(sys.version_info.major == 2, "not supported on python2")
+     def test_zombie_process(self):
+         def succeed_or_zombie_p_exc(fun):
+             try: