diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 41ef824afc2a7..3fae0fbe7d2a0 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -807,24 +807,17 @@ def delete(self, loc) -> Index:  # type: ignore[override]
                 return self[1:]
             if loc == -1 or loc == len(self) - 1:
                 return self[:-1]
+            if len(self) == 3 and (loc == 1 or loc == -2):
+                return self[::2]
 
         elif lib.is_list_like(loc):
             slc = lib.maybe_indices_to_slice(np.asarray(loc, dtype=np.intp), len(self))
-            if isinstance(slc, slice) and slc.step is not None and slc.step < 0:
-                rng = range(len(self))[slc][::-1]
-                slc = slice(rng.start, rng.stop, rng.step)
-
-            if isinstance(slc, slice) and slc.step in [1, None]:
-                # Note: maybe_indices_to_slice will never return a slice
-                #  with 'slc.start is None'; may have slc.stop None in cases
-                #  with negative step
-                if slc.start == 0:
-                    return self[slc.stop :]
-                elif slc.stop in [len(self), None]:
-                    return self[: slc.start]
-
-                # TODO: more generally, self.difference(self[slc]),
-                #  once _difference is better about retaining RangeIndex
+
+            if isinstance(slc, slice):
+                # defer to RangeIndex._difference, which is optimized to return
+                #  a RangeIndex whenever possible
+                other = self[slc]
+                return self.difference(other, sort=False)
 
         return super().delete(loc)
 
diff --git a/pandas/tests/indexes/ranges/test_range.py b/pandas/tests/indexes/ranges/test_range.py
index d58dff191cc73..277f686a8487a 100644
--- a/pandas/tests/indexes/ranges/test_range.py
+++ b/pandas/tests/indexes/ranges/test_range.py
@@ -178,6 +178,15 @@ def test_delete_preserves_rangeindex(self):
         result = idx.delete(1)
         tm.assert_index_equal(result, expected, exact=True)
 
+    def test_delete_preserves_rangeindex_middle(self):
+        idx = Index(range(3), name="foo")
+        result = idx.delete(1)
+        expected = idx[::2]
+        tm.assert_index_equal(result, expected, exact=True)
+
+        result = idx.delete(-2)
+        tm.assert_index_equal(result, expected, exact=True)
+
     def test_delete_preserves_rangeindex_list_at_end(self):
         idx = RangeIndex(0, 6, 1)