diff --git a/stdlib/logging/__init__.pyi b/stdlib/logging/__init__.pyi
index 59822ab3c..135d64a38 100644
--- a/stdlib/logging/__init__.pyi
+++ b/stdlib/logging/__init__.pyi
@@ -706,7 +706,7 @@ else:
     ) -> None: ...
 
 def shutdown(handlerList: Sequence[Any] = ...) -> None: ...  # handlerList is undocumented
-def setLoggerClass(klass: type) -> None: ...
+def setLoggerClass(klass: Type[Logger]) -> None: ...
 def captureWarnings(capture: bool) -> None: ...
 def setLogRecordFactory(factory: Callable[..., LogRecord]) -> None: ...
 
diff --git a/stdlib/sqlite3/dbapi2.pyi b/stdlib/sqlite3/dbapi2.pyi
index 51def5406..0eaab5eff 100644
--- a/stdlib/sqlite3/dbapi2.pyi
+++ b/stdlib/sqlite3/dbapi2.pyi
@@ -1,7 +1,7 @@
 import os
 import sys
 from datetime import date, datetime, time
-from typing import Any, Callable, Generator, Iterable, Iterator, List, Optional, Text, Tuple, Type, TypeVar, Union
+from typing import Any, Callable, Generator, Iterable, Iterator, List, Optional, Protocol, Text, Tuple, Type, TypeVar, Union
 
 _T = TypeVar("_T")
 
@@ -113,6 +113,10 @@ if sys.version_info < (3, 8):
         def display(self, *args, **kwargs) -> None: ...
         def get(self, *args, **kwargs) -> None: ...
 
+class _AggregateProtocol(Protocol):
+    def step(self, value: int) -> None: ...
+    def finalize(self) -> int: ...
+
 class Connection(object):
     DataError: Any
     DatabaseError: Any
@@ -132,7 +136,7 @@ class Connection(object):
     def __init__(self, *args: Any, **kwargs: Any) -> None: ...
     def close(self) -> None: ...
     def commit(self) -> None: ...
-    def create_aggregate(self, name: str, num_params: int, aggregate_class: type) -> None: ...
+    def create_aggregate(self, name: str, num_params: int, aggregate_class: Callable[[], _AggregateProtocol]) -> None: ...
     def create_collation(self, name: str, callable: Any) -> None: ...
     if sys.version_info >= (3, 8):
         def create_function(self, name: str, num_params: int, func: Any, *, deterministic: bool = ...) -> None: ...