diff --git a/pydantic/_internal/_generics.py b/pydantic/_internal/_generics.py
index 876b5e7be5..5015ce7aec 100644
--- a/pydantic/_internal/_generics.py
+++ b/pydantic/_internal/_generics.py
@@ -15,7 +15,7 @@
 from ._core_utils import get_type_ref
 from ._forward_ref import PydanticRecursiveRef
 from ._typing_extra import TypeVarType, typing_base
-from ._utils import all_identical, is_basemodel
+from ._utils import all_identical, is_model_class
 
 if sys.version_info >= (3, 10):
     from typing import _UnionGenericAlias  # type: ignore[attr-defined]
@@ -197,7 +197,7 @@ def iter_contained_typevars(v: Any) -> Iterator[TypeVarType]:
     """
     if isinstance(v, TypeVar):
         yield v
-    elif is_basemodel(v):
+    elif is_model_class(v):
         yield from v.__pydantic_generic_metadata__['parameters']
     elif isinstance(v, (DictValues, list)):
         for var in v:
@@ -316,7 +316,7 @@ def replace_types(type_: Any, type_map: Mapping[Any, Any] | None) -> Any:
     # We handle pydantic generic models separately as they don't have the same
     # semantics as "typing" classes or generic aliases
 
-    if not origin_type and is_basemodel(type_):
+    if not origin_type and is_model_class(type_):
         parameters = type_.__pydantic_generic_metadata__['parameters']
         if not parameters:
             return type_
diff --git a/pydantic/_internal/_utils.py b/pydantic/_internal/_utils.py
index 16d921e9c3..5e6182aaa7 100644
--- a/pydantic/_internal/_utils.py
+++ b/pydantic/_internal/_utils.py
@@ -79,17 +79,13 @@ def lenient_issubclass(cls: Any, class_or_tuple: Any) -> bool:  # pragma: no cov
         raise  # pragma: no cover
 
 
-def is_basemodel(cls: Any) -> TypeGuard[type[BaseModel]]:
-    """We can remove this function and go back to using lenient_issubclass, but this is nice because it
-    ensures that we get proper type-checking, which lenient_issubclass doesn't provide.
-
-    Would be nice if there was a lenient_issubclass-equivalent in typing_extensions, or otherwise
-    a way to define such a function that would support proper type-checking; maybe we should bring it up
-    at the typing summit..
+def is_model_class(cls: Any) -> TypeGuard[type[BaseModel]]:
+    """Returns true if cls is a _proper_ subclass of BaseModel, and provides proper type-checking,
+    unlike raw calls to lenient_issubclass.
     """
     from ..main import BaseModel
 
-    return lenient_issubclass(cls, BaseModel)
+    return lenient_issubclass(cls, BaseModel) and cls is not BaseModel
 
 
 def is_valid_identifier(identifier: str) -> bool:
diff --git a/tests/test_generics.py b/tests/test_generics.py
index 512b411cb1..434035d40f 100644
--- a/tests/test_generics.py
+++ b/tests/test_generics.py
@@ -2551,3 +2551,13 @@ class ParamSpecGenericModel(BaseModel, Generic[P]):
         my_generic: MyGenericParamSpecClass[P]
 
         model_config = dict(arbitrary_types_allowed=True)
+
+
+def test_parametrize_with_basemodel():
+    T = TypeVar('T')
+
+    class SimpleGenericModel(BaseModel, Generic[T]):
+        pass
+
+    class Concrete(SimpleGenericModel[BaseModel]):
+        pass