diff --git a/src/_pytest/_code/code.py b/src/_pytest/_code/code.py
index 48a8685bd..0288d7a54 100644
--- a/src/_pytest/_code/code.py
+++ b/src/_pytest/_code/code.py
@@ -725,13 +725,22 @@ class ExceptionInfo(Generic[E]):
         exc_group: BaseExceptionGroup[BaseException],
         expected_exception: Union[Type[BaseException], Tuple[Type[BaseException], ...]],
         match: Union[str, Pattern[str], None],
-        recursive: bool = False,
+        target_depth: Optional[int] = None,
+        current_depth: int = 1,
     ) -> bool:
         """Return `True` if a `BaseExceptionGroup` contains a matching exception."""
+        if (target_depth is not None) and (current_depth > target_depth):
+            # already descended past the target depth
+            return False
         for exc in exc_group.exceptions:
-            if recursive and isinstance(exc, BaseExceptionGroup):
-                if self._group_contains(exc, expected_exception, match, recursive):
+            if isinstance(exc, BaseExceptionGroup):
+                if self._group_contains(
+                    exc, expected_exception, match, target_depth, current_depth + 1
+                ):
                     return True
+            if (target_depth is not None) and (current_depth != target_depth):
+                # not at the target depth, no match
+                continue
             if not isinstance(exc, expected_exception):
                 continue
             if match is not None:
@@ -744,8 +753,9 @@ class ExceptionInfo(Generic[E]):
     def group_contains(
         self,
         expected_exception: Union[Type[BaseException], Tuple[Type[BaseException], ...]],
+        *,
         match: Union[str, Pattern[str], None] = None,
-        recursive: bool = False,
+        depth: Optional[int] = None,
     ) -> bool:
         """Check whether a captured exception group contains a matching exception.
 
@@ -762,13 +772,16 @@ class ExceptionInfo(Generic[E]):
             To match a literal string that may contain :ref:`special characters
             <re-syntax>`, the pattern can first be escaped with :func:`re.escape`.
 
-        :param bool recursive:
-            If `True`, search will descend recursively into any nested exception groups.
-            If `False`, only the top exception group will be searched.
+        :param Optional[int] depth:
+            If `None`, will search for a matching exception at any nesting depth.
+            If >= 1, will only match an exception if it's at the specified depth (depth = 1 being
+            the exceptions contained within the topmost exception group).
         """
         msg = "Captured exception is not an instance of `BaseExceptionGroup`"
         assert isinstance(self.value, BaseExceptionGroup), msg
-        return self._group_contains(self.value, expected_exception, match, recursive)
+        msg = "`depth` must be >= 1 if specified"
+        assert (depth is None) or (depth >= 1), msg
+        return self._group_contains(self.value, expected_exception, match, depth)
 
 
 @dataclasses.dataclass
diff --git a/testing/code/test_excinfo.py b/testing/code/test_excinfo.py
index 4e6e89a20..89beefce5 100644
--- a/testing/code/test_excinfo.py
+++ b/testing/code/test_excinfo.py
@@ -472,36 +472,66 @@ class TestGroupContains:
             raise exc_group
         assert not exc_info.group_contains(RuntimeError, match=r"^exception message$")
 
-    def test_contains_exception_type_recursive(self) -> None:
+    def test_contains_exception_type_unlimited_depth(self) -> None:
         exc_group = ExceptionGroup("", [ExceptionGroup("", [RuntimeError()])])
         with pytest.raises(ExceptionGroup) as exc_info:
             raise exc_group
-        assert exc_info.group_contains(RuntimeError, recursive=True)
+        assert exc_info.group_contains(RuntimeError)
 
-    def test_doesnt_contain_exception_type_nonrecursive(self) -> None:
+    def test_contains_exception_type_at_depth_1(self) -> None:
+        exc_group = ExceptionGroup("", [RuntimeError()])
+        with pytest.raises(ExceptionGroup) as exc_info:
+            raise exc_group
+        assert exc_info.group_contains(RuntimeError, depth=1)
+
+    def test_doesnt_contain_exception_type_past_depth(self) -> None:
         exc_group = ExceptionGroup("", [ExceptionGroup("", [RuntimeError()])])
         with pytest.raises(ExceptionGroup) as exc_info:
             raise exc_group
-        assert not exc_info.group_contains(RuntimeError)
+        assert not exc_info.group_contains(RuntimeError, depth=1)
 
-    def test_contains_exception_match_recursive(self) -> None:
+    def test_contains_exception_type_specific_depth(self) -> None:
+        exc_group = ExceptionGroup("", [ExceptionGroup("", [RuntimeError()])])
+        with pytest.raises(ExceptionGroup) as exc_info:
+            raise exc_group
+        assert exc_info.group_contains(RuntimeError, depth=2)
+
+    def test_contains_exception_match_unlimited_depth(self) -> None:
+        exc_group = ExceptionGroup(
+            "", [ExceptionGroup("", [RuntimeError("exception message")])]
+        )
+        with pytest.raises(ExceptionGroup) as exc_info:
+            raise exc_group
+        assert exc_info.group_contains(RuntimeError, match=r"^exception message$")
+
+    def test_contains_exception_match_at_depth_1(self) -> None:
+        exc_group = ExceptionGroup("", [RuntimeError("exception message")])
+        with pytest.raises(ExceptionGroup) as exc_info:
+            raise exc_group
+        assert exc_info.group_contains(
+            RuntimeError, match=r"^exception message$", depth=1
+        )
+
+    def test_doesnt_contain_exception_match_past_depth(self) -> None:
+        exc_group = ExceptionGroup(
+            "", [ExceptionGroup("", [RuntimeError("exception message")])]
+        )
+        with pytest.raises(ExceptionGroup) as exc_info:
+            raise exc_group
+        assert not exc_info.group_contains(
+            RuntimeError, match=r"^exception message$", depth=1
+        )
+
+    def test_contains_exception_match_specific_depth(self) -> None:
         exc_group = ExceptionGroup(
             "", [ExceptionGroup("", [RuntimeError("exception message")])]
         )
         with pytest.raises(ExceptionGroup) as exc_info:
             raise exc_group
         assert exc_info.group_contains(
-            RuntimeError, match=r"^exception message$", recursive=True
+            RuntimeError, match=r"^exception message$", depth=2
         )
 
-    def test_doesnt_contain_exception_match_nonrecursive(self) -> None:
-        exc_group = ExceptionGroup(
-            "", [ExceptionGroup("", [RuntimeError("message that will not match")])]
-        )
-        with pytest.raises(ExceptionGroup) as exc_info:
-            raise exc_group
-        assert not exc_info.group_contains(RuntimeError, match=r"^exception message$")
-
 
 class TestFormattedExcinfo:
     @pytest.fixture