diff --git a/redis/asyncio/connection.py b/redis/asyncio/connection.py
index 456fb4563b..00865515ab 100644
--- a/redis/asyncio/connection.py
+++ b/redis/asyncio/connection.py
@@ -998,10 +998,8 @@ def __init__(
         self.connection_kwargs = connection_kwargs
         self.max_connections = max_connections
 
-        self._created_connections: int
-        self._available_connections: List[AbstractConnection]
-        self._in_use_connections: Set[AbstractConnection]
-        self.reset()  # lgtm [py/init-calls-subclass]
+        self._available_connections: List[AbstractConnection] = []
+        self._in_use_connections: Set[AbstractConnection] = set()
         self.encoder_class = self.connection_kwargs.get("encoder_class", Encoder)
 
     def __repr__(self):
@@ -1011,7 +1009,6 @@ def __repr__(self):
         )
 
     def reset(self):
-        self._created_connections = 0
         self._available_connections = []
         self._in_use_connections = set()
 
@@ -1019,7 +1016,7 @@ def can_get_connection(self) -> bool:
         """Return True if a connection can be retrieved from the pool."""
         return (
             self._available_connections
-            or self._created_connections < self.max_connections
+            or len(self._in_use_connections) < self.max_connections
         )
 
     async def get_connection(self, command_name, *keys, **options):
@@ -1027,27 +1024,14 @@ async def get_connection(self, command_name, *keys, **options):
         try:
             connection = self._available_connections.pop()
         except IndexError:
+            if len(self._in_use_connections) >= self.max_connections:
+                raise ConnectionError("Too many connections") from None
             connection = self.make_connection()
         self._in_use_connections.add(connection)
 
         try:
-            # ensure this connection is connected to Redis
-            await connection.connect()
-            # connections that the pool provides should be ready to send
-            # a command. if not, the connection was either returned to the
-            # pool before all data has been read or the socket has been
-            # closed. either way, reconnect and verify everything is good.
-            try:
-                if await connection.can_read_destructive():
-                    raise ConnectionError("Connection has data") from None
-            except (ConnectionError, OSError):
-                await connection.disconnect()
-                await connection.connect()
-                if await connection.can_read_destructive():
-                    raise ConnectionError("Connection not ready") from None
+            await self.ensure_connection(connection)
         except BaseException:
-            # release the connection back to the pool so that we don't
-            # leak it
             await self.release(connection)
             raise
 
@@ -1063,12 +1047,25 @@ def get_encoder(self):
         )
 
     def make_connection(self):
-        """Create a new connection"""
-        if self._created_connections >= self.max_connections:
-            raise ConnectionError("Too many connections")
-        self._created_connections += 1
+        """Create a new connection.  Can be overridden by child classes."""
         return self.connection_class(**self.connection_kwargs)
 
+    async def ensure_connection(self, connection: AbstractConnection):
+        """Ensure that the connection object is connected and valid"""
+        await connection.connect()
+        # connections that the pool provides should be ready to send
+        # a command. if not, the connection was either returned to the
+        # pool before all data has been read or the socket has been
+        # closed. either way, reconnect and verify everything is good.
+        try:
+            if await connection.can_read_destructive():
+                raise ConnectionError("Connection has data") from None
+        except (ConnectionError, OSError):
+            await connection.disconnect()
+            await connection.connect()
+            if await connection.can_read_destructive():
+                raise ConnectionError("Connection not ready") from None
+
     async def release(self, connection: AbstractConnection):
         """Releases the connection back to the pool"""
         # Connections should always be returned to the correct pool,