diff --git a/pungi/gather_dnf.py b/pungi/gather_dnf.py
index d7208391..7ddbaf4b 100644
--- a/pungi/gather_dnf.py
+++ b/pungi/gather_dnf.py
@@ -593,10 +593,13 @@ class Gather(GatherBase):
                     # fallback / default
                     pull_native = True
 
-                if pull_native:
-                    fulltree_pkgs = native_fulltree_pkgs
-                else:
-                    fulltree_pkgs = multilib_fulltree_pkgs
+                # We pull packages determined by `pull_native`, or everything
+                # if we're greedy
+                fulltree_pkgs = []
+                if pull_native or self.opts.greedy_method == 'all':
+                    fulltree_pkgs.extend(native_fulltree_pkgs)
+                if not pull_native or self.opts.greedy_method == 'all':
+                    fulltree_pkgs.extend(multilib_fulltree_pkgs)
 
                 # always pull all noarch subpackages
                 fulltree_pkgs += noarch_fulltree_pkgs
diff --git a/tests/test_gather.py b/tests/test_gather.py
index f12023a3..634d6948 100644
--- a/tests/test_gather.py
+++ b/tests/test_gather.py
@@ -1688,18 +1688,10 @@ class DNFDepsolvingTestCase(DepsolvingBase, unittest.TestCase):
         dummy-bash-debuginfo.x86_64 as well.
         """
 
-    @unittest.skip('Full does not pull in dummy-nscd.i686')
-    def test_bash_multilib_greedy(self):
-        pass
-
     @unittest.skip('DNF code does not support NVR as input')
     def test_bash_older(self):
         pass
 
-    @unittest.skip('Misses dummy-nscd.i686')
-    def test_bash_multilib_filter_greedy(self):
-        pass
-
     @unittest.skip('Not implemented yet')
     def test_smtpdaemon_greedy_all_explicit_sendmail(self):
         pass