diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index d87e6ba1c3..f02ebcc43b 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -81,6 +81,12 @@ using `invoke standalone-tests`; similarly, RedisCluster tests can be run by usi
 Each run of tests starts and stops the various dockers required. Sometimes
 things get stuck, an `invoke clean` can help.
 
+## Linting and Formatting
+
+Call `invoke linters` to run linters without also running tests. This command will
+only report issues, not fix them automatically. Run `invoke formatters` to
+automatically format your code.
+
 ## Documentation
 
 If relevant, update the code documentation, via docstrings, or in `/docs`.
diff --git a/redis/asyncio/client.py b/redis/asyncio/client.py
index 4254441073..bdfb739788 100644
--- a/redis/asyncio/client.py
+++ b/redis/asyncio/client.py
@@ -362,6 +362,12 @@ def __init__(
         # on a set of redis commands
         self._single_conn_lock = asyncio.Lock()
 
+        # When used as an async context manager, we need to increment and decrement
+        # a usage counter so that we can close the connection pool when no one is
+        # using the client.
+        self._usage_counter = 0
+        self._usage_lock = asyncio.Lock()
+
     def __repr__(self):
         return (
             f"<{self.__class__.__module__}.{self.__class__.__name__}"
@@ -562,10 +568,40 @@ def client(self) -> "Redis":
         )
 
     async def __aenter__(self: _RedisT) -> _RedisT:
-        return await self.initialize()
+        """
+        Async context manager entry. Increments a usage counter so that the
+        connection pool is only closed (via aclose()) when no context is using
+        the client.
+        """
+        async with self._usage_lock:
+            self._usage_counter += 1
+        try:
+            # Initialize the client (i.e. establish connection, etc.)
+            return await self.initialize()
+        except Exception:
+            # If initialization fails, decrement the counter to keep it in sync
+            async with self._usage_lock:
+                self._usage_counter -= 1
+            raise
+
+    async def _decrement_usage(self) -> int:
+        """
+        Helper coroutine to decrement the usage counter while holding the lock.
+        Returns the new value of the usage counter.
+        """
+        async with self._usage_lock:
+            self._usage_counter -= 1
+            return self._usage_counter
 
     async def __aexit__(self, exc_type, exc_value, traceback):
-        await self.aclose()
+        """
+        Async context manager exit. Decrements a usage counter. If this is the
+        last exit (counter becomes zero), the client closes its connection pool.
+        """
+        current_usage = await asyncio.shield(self._decrement_usage())
+        if current_usage == 0:
+            # This was the last active context, so disconnect the pool.
+            await asyncio.shield(self.aclose())
 
     _DEL_MESSAGE = "Unclosed Redis client"
 
diff --git a/redis/asyncio/cluster.py b/redis/asyncio/cluster.py
index 87a2c16afa..b13a9ca6f5 100644
--- a/redis/asyncio/cluster.py
+++ b/redis/asyncio/cluster.py
@@ -379,6 +379,12 @@ def __init__(
         self._initialize = True
         self._lock: Optional[asyncio.Lock] = None
 
+        # When used as an async context manager, we need to increment and decrement
+        # a usage counter so that we can close the connection pool when no one is
+        # using the client.
+        self._usage_counter = 0
+        self._usage_lock = asyncio.Lock()
+
     async def initialize(self) -> "RedisCluster":
         """Get all nodes from startup nodes & creates connections if not initialized."""
         if self._initialize:
@@ -415,10 +421,40 @@ async def close(self) -> None:
         await self.aclose()
 
     async def __aenter__(self) -> "RedisCluster":
-        return await self.initialize()
+        """
+        Async context manager entry. Increments a usage counter so that the
+        connection pool is only closed (via aclose()) when no context is using
+        the client.
+        """
+        async with self._usage_lock:
+            self._usage_counter += 1
+        try:
+            # Initialize the client (i.e. establish connection, etc.)
+            return await self.initialize()
+        except Exception:
+            # If initialization fails, decrement the counter to keep it in sync
+            async with self._usage_lock:
+                self._usage_counter -= 1
+            raise
 
-    async def __aexit__(self, exc_type: None, exc_value: None, traceback: None) -> None:
-        await self.aclose()
+    async def _decrement_usage(self) -> int:
+        """
+        Helper coroutine to decrement the usage counter while holding the lock.
+        Returns the new value of the usage counter.
+        """
+        async with self._usage_lock:
+            self._usage_counter -= 1
+            return self._usage_counter
+
+    async def __aexit__(self, exc_type, exc_value, traceback):
+        """
+        Async context manager exit. Decrements a usage counter. If this is the
+        last exit (counter becomes zero), the client closes its connection pool.
+        """
+        current_usage = await asyncio.shield(self._decrement_usage())
+        if current_usage == 0:
+            # This was the last active context, so disconnect the pool.
+            await asyncio.shield(self.aclose())
 
     def __await__(self) -> Generator[Any, None, "RedisCluster"]:
         return self.initialize().__await__()
diff --git a/tasks.py b/tasks.py
index f7b728aed4..f318da5608 100644
--- a/tasks.py
+++ b/tasks.py
@@ -33,6 +33,12 @@ def linters(c):
     run("vulture redis whitelist.py --min-confidence 80")
     run("flynt --fail-on-change --dry-run tests redis")
 
+@task
+def formatters(c):
+    """Format code"""
+    run("black --target-version py37 tests redis")
+    run("isort tests redis")
+
 
 @task
 def all_tests(c):
diff --git a/tests/test_asyncio/test_usage_counter.py b/tests/test_asyncio/test_usage_counter.py
new file mode 100644
index 0000000000..566ec6b4d3
--- /dev/null
+++ b/tests/test_asyncio/test_usage_counter.py
@@ -0,0 +1,16 @@
+import asyncio
+
+import pytest
+
+
+@pytest.mark.asyncio
+async def test_usage_counter(r):
+    async def dummy_task():
+        async with r:
+            await asyncio.sleep(0.01)
+
+    tasks = [dummy_task() for _ in range(20)]
+    await asyncio.gather(*tasks)
+
+    # After all tasks have completed, the usage counter should be back to zero.
+    assert r._usage_counter == 0