diff --git a/aiosqlite/cursor.py b/aiosqlite/cursor.py
index 6932874..a2990ba 100644
--- a/aiosqlite/cursor.py
+++ b/aiosqlite/cursor.py
@@ -19,7 +19,7 @@ def __aiter__(self) -> AsyncIterator[sqlite3.Row]:
         """The cursor proxy is also an async iterator."""
         return self._fetch_chunked()
 
-    async def _fetch_chunked(self):
+    async def _fetch_chunked(self) -> AsyncIterator[sqlite3.Row]:
         while True:
             rows = await self.fetchmany(self.iter_chunk_size)
             if not rows:
@@ -56,14 +56,14 @@ async def fetchone(self) -> Optional[sqlite3.Row]:
         """Fetch a single row."""
         return await self._execute(self._cursor.fetchone)
 
-    async def fetchmany(self, size: Optional[int] = None) -> Iterable[sqlite3.Row]:
+    async def fetchmany(self, size: Optional[int] = None) -> list[sqlite3.Row]:
         """Fetch up to `cursor.arraysize` number of rows."""
         args: tuple[int, ...] = ()
         if size is not None:
             args = (size,)
         return await self._execute(self._cursor.fetchmany, *args)
 
-    async def fetchall(self) -> Iterable[sqlite3.Row]:
+    async def fetchall(self) -> list[sqlite3.Row]:
         """Fetch all remaining rows."""
         return await self._execute(self._cursor.fetchall)
 
@@ -103,8 +103,8 @@ def row_factory(self, factory: Optional[type]) -> None:
     def connection(self) -> sqlite3.Connection:
         return self._cursor.connection
 
-    async def __aenter__(self):
+    async def __aenter__(self) -> "Cursor":
         return self
 
-    async def __aexit__(self, exc_type, exc_val, exc_tb):
+    async def __aexit__(self, exc_type, exc_val, exc_tb) -> None:
         await self.close()
diff --git a/aiosqlite/tests/smoke.py b/aiosqlite/tests/smoke.py
index 046f9b7..e8e5017 100644
--- a/aiosqlite/tests/smoke.py
+++ b/aiosqlite/tests/smoke.py
@@ -126,6 +126,37 @@ async def test_iterable_cursor(self):
 
         assert len(rows) == 10
 
+    async def test_iterable_cursor_after_fetchmany(self):
+        async with aiosqlite.connect(self.db) as db:
+            cursor = await db.cursor()
+            await cursor.execute(
+                "create table iterable_cursor_after_fetchmany "
+                "(i integer primary key asc, k integer)"
+            )
+            await cursor.executemany(
+                "insert into iterable_cursor_after_fetchmany (k) values (?)",
+                [[i] for i in range(5)],
+            )
+            await db.commit()
+
+        async with aiosqlite.connect(self.db) as db:
+            cursor = await db.execute(
+                "select * from iterable_cursor_after_fetchmany"
+            )
+            first_two = await cursor.fetchmany(2)
+            self.assertEqual(len(first_two), 2)
+            self.assertEqual(first_two[0], (1, 0))
+            self.assertEqual(first_two[1], (2, 1))
+
+            remaining = []
+            async for row in cursor:
+                remaining.append(row)
+
+            self.assertEqual(len(remaining), 3)
+            self.assertEqual(remaining[0], (3, 2))
+            self.assertEqual(remaining[1], (4, 3))
+            self.assertEqual(remaining[2], (5, 4))
+
     async def test_multi_loop_usage(self):
         results = {}