diff --git a/_pytest/python.py b/_pytest/python.py
index 8438ca428..88c7d1a39 100644
--- a/_pytest/python.py
+++ b/_pytest/python.py
@@ -1818,7 +1818,7 @@ class FixtureManager:
                 if fixturedef.params is not None:
                     func_params = getattr(getattr(metafunc.function, 'parametrize', None), 'args', [[None]])
                     # skip directly parametrized arguments
-                    if argname not in func_params and argname not in func_params[0]:
+                    if argname not in func_params:
                         metafunc.parametrize(argname, fixturedef.params,
                                              indirect=True, scope=fixturedef.scope,
                                              ids=fixturedef.ids)
diff --git a/testing/python/collect.py b/testing/python/collect.py
index 97250028a..029b0b693 100644
--- a/testing/python/collect.py
+++ b/testing/python/collect.py
@@ -412,9 +412,19 @@ class TestFunction:
                                      ['overridden'])
             def test_overridden_via_param(value):
                 assert value == 'overridden'
+
+            @pytest.mark.parametrize('somevalue', ['overridden'])
+            def test_not_overridden(value, somevalue):
+                assert value == 'value'
+                assert somevalue == 'overridden'
+
+            @pytest.mark.parametrize('other,value', [('foo', 'overridden')])
+            def test_overridden_via_multiparam(other, value):
+                assert other == 'foo'
+                assert value == 'overridden'
         """)
         rec = testdir.inline_run()
-        rec.assertoutcome(passed=1)
+        rec.assertoutcome(passed=3)
 
 
     def test_parametrize_overrides_parametrized_fixture(self, testdir):
diff --git a/testing/python/fixture.py b/testing/python/fixture.py
index 8bf738c5d..48f52d2a0 100644
--- a/testing/python/fixture.py
+++ b/testing/python/fixture.py
@@ -1598,6 +1598,22 @@ class TestFixtureMarker:
         reprec = testdir.inline_run()
         reprec.assertoutcome(passed=4)
 
+    def test_multiple_parametrization_issue_736(self, testdir):
+        testdir.makepyfile("""
+            import pytest
+
+            @pytest.fixture(params=[1,2,3])
+            def foo(request):
+                return request.param
+
+            @pytest.mark.parametrize('foobar', [4,5,6])
+            def test_issue(foo, foobar):
+                assert foo in [1,2,3]
+                assert foobar in [4,5,6]
+        """)
+        reprec = testdir.inline_run()
+        reprec.assertoutcome(passed=9)
+
     def test_scope_session(self, testdir):
         testdir.makepyfile("""
             import pytest