diff --git a/python/cudf/cudf/core/groupby/groupby.py b/python/cudf/cudf/core/groupby/groupby.py
index 61fe20636f0..c1060d5f505 100644
--- a/python/cudf/cudf/core/groupby/groupby.py
+++ b/python/cudf/cudf/core/groupby/groupby.py
@@ -110,6 +110,7 @@ def cumcount(self):
             )
             .groupby(self.grouping, sort=self._sort)
             .agg("cumcount")
+            .reset_index(drop=True)
         )
 
     @cached_property
@@ -225,9 +226,10 @@ def nth(self, n):
         """
         Return the nth row from each group.
         """
-        result = self.agg(lambda x: x.nth(n))
-        sizes = self.size()
-        return result[n < sizes]
+        result = self.agg(lambda x: x.nth(n)).sort_index()
+        sizes = self.size().sort_index()
+
+        return result[sizes > n]
 
     def serialize(self):
         header = {}
diff --git a/python/cudf/cudf/tests/test_groupby.py b/python/cudf/cudf/tests/test_groupby.py
index d1458c72770..2430b0da5ef 100644
--- a/python/cudf/cudf/tests/test_groupby.py
+++ b/python/cudf/cudf/tests/test_groupby.py
@@ -30,14 +30,28 @@
 _index_type_aggs = {"count", "idxmin", "idxmax", "cumcount"}
 
 
-def assert_groupby_results_equal(expect, got, sort=True, **kwargs):
+def assert_groupby_results_equal(
+    expect, got, sort=True, as_index=True, by=None, **kwargs
+):
     # Because we don't sort by index by default in groupby,
     # sort expect and got by index before comparing
     if sort:
-        expect = expect.sort_index()
-        got = got.sort_index()
-    else:
-        assert_eq(expect.sort_index(), got.sort_index(), **kwargs)
+        if as_index:
+            expect = expect.sort_index()
+            got = got.sort_index()
+        else:
+            assert by is not None
+            if isinstance(expect, (pd.DataFrame, cudf.DataFrame)):
+                expect = expect.sort_values(by=by).reset_index(drop=True)
+            else:
+                expect = expect.sort_values().reset_index(drop=True)
+
+            if isinstance(got, cudf.DataFrame):
+                got = got.sort_values(by=by).reset_index(drop=True)
+            else:
+                got = got.sort_values().reset_index(drop=True)
+
+    assert_eq(expect, got, **kwargs)
 
 
 def make_frame(
@@ -201,10 +215,16 @@ def test_groupby_getitem_getattr(as_index):
     pdf = pd.DataFrame({"x": [1, 3, 1], "y": [1, 2, 3], "z": [1, 4, 5]})
     gdf = cudf.from_pandas(pdf)
     assert_groupby_results_equal(
-        pdf.groupby("x")["y"].sum(), gdf.groupby("x")["y"].sum(),
+        pdf.groupby("x")["y"].sum(),
+        gdf.groupby("x")["y"].sum(),
+        as_index=as_index,
+        by="x",
     )
     assert_groupby_results_equal(
-        pdf.groupby("x").y.sum(), gdf.groupby("x").y.sum(),
+        pdf.groupby("x").y.sum(),
+        gdf.groupby("x").y.sum(),
+        as_index=as_index,
+        by="x",
     )
     assert_groupby_results_equal(
         pdf.groupby("x")[["y"]].sum(), gdf.groupby("x")[["y"]].sum(),
@@ -212,6 +232,8 @@ def test_groupby_getitem_getattr(as_index):
     assert_groupby_results_equal(
         pdf.groupby(["x", "y"], as_index=as_index).sum(),
         gdf.groupby(["x", "y"], as_index=as_index).sum(),
+        as_index=as_index,
+        by=["x", "y"],
     )
 
 
@@ -1088,7 +1110,13 @@ def test_groupby_datetime(nelem, as_index, agg):
     else:
         pdres = pdg.agg({"datetime": agg})
         gdres = gdg.agg({"datetime": agg})
-    assert_groupby_results_equal(pdres, gdres, check_dtype=check_dtype)
+    assert_groupby_results_equal(
+        pdres,
+        gdres,
+        check_dtype=check_dtype,
+        as_index=as_index,
+        by=["datetime"],
+    )
 
 
 def test_groupby_dropna():
@@ -1349,6 +1377,8 @@ def test_reset_index_after_empty_groupby():
     assert_groupby_results_equal(
         pdf.groupby("a").sum().reset_index(),
         gdf.groupby("a").sum().reset_index(),
+        as_index=False,
+        by="a",
     )