diff --git a/src/Kestrel.Core/Internal/Http/HttpProtocol.cs b/src/Kestrel.Core/Internal/Http/HttpProtocol.cs
index 6acbc0e378..b51d3ce6b8 100644
--- a/src/Kestrel.Core/Internal/Http/HttpProtocol.cs
+++ b/src/Kestrel.Core/Internal/Http/HttpProtocol.cs
@@ -1131,7 +1131,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal.Http
             // chunked is applied to a response payload body, the sender MUST either
             // apply chunked as the final transfer coding or terminate the message
             // by closing the connection.
-            if (hasTransferEncoding && 
+            if (hasTransferEncoding &&
                 HttpHeaders.GetFinalTransferCoding(responseHeaders.HeaderTransferEncoding) != TransferCoding.Chunked)
             {
                 _keepAlive = false;
diff --git a/src/Kestrel.Core/Internal/Http2/Http2Connection.cs b/src/Kestrel.Core/Internal/Http2/Http2Connection.cs
index 7ffa068d88..cd5b95caed 100644
--- a/src/Kestrel.Core/Internal/Http2/Http2Connection.cs
+++ b/src/Kestrel.Core/Internal/Http2/Http2Connection.cs
@@ -79,6 +79,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal.Http2
         private readonly object _stateLock = new object();
         private int _highestOpenedStreamId;
         private Http2ConnectionState _state = Http2ConnectionState.Open;
+        private readonly TaskCompletionSource<object> _streamsCompleted = new TaskCompletionSource<object>(TaskCreationOptions.RunContinuationsAsynchronously);
 
         private readonly ConcurrentDictionary<int, Http2Stream> _streams = new ConcurrentDictionary<int, Http2Stream>();
 
@@ -256,6 +257,11 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal.Http2
                             _frameWriter.WriteGoAwayAsync(_highestOpenedStreamId, errorCode);
                             UpdateState(Http2ConnectionState.Closed);
                         }
+
+                        if (_streams.IsEmpty)
+                        {
+                            _streamsCompleted.TrySetResult(null);
+                        }
                     }
 
                     // Ensure aborting each stream doesn't result in unnecessary WINDOW_UPDATE frames being sent.
@@ -266,6 +272,8 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal.Http2
                         stream.Abort(connectionError);
                     }
 
+                    await _streamsCompleted.Task;
+
                     _frameWriter.Complete();
                 }
                 catch
@@ -891,13 +899,19 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Internal.Http2
             {
                 _streams.TryRemove(streamId, out _);
 
-                if (_state == Http2ConnectionState.Closing && _streams.IsEmpty)
+                if (_streams.IsEmpty)
                 {
-                    _frameWriter.WriteGoAwayAsync(_highestOpenedStreamId, Http2ErrorCode.NO_ERROR);
-                    UpdateState(Http2ConnectionState.Closed);
+                    if (_state == Http2ConnectionState.Closing)
+                    {
+                        _frameWriter.WriteGoAwayAsync(_highestOpenedStreamId, Http2ErrorCode.NO_ERROR);
+                        UpdateState(Http2ConnectionState.Closed);
 
-                    // Wake up request processing loop so the connection can complete if there are no pending requests
-                    Input.CancelPendingRead();
+                        // Wake up request processing loop so the connection can complete if there are no pending requests
+                        Input.CancelPendingRead();
+                    }
+
+                    // Complete the task waiting on all streams to finish
+                    _streamsCompleted.TrySetResult(null);
                 }
             }
         }
diff --git a/test/Kestrel.Core.Tests/Http2ConnectionTests.cs b/test/Kestrel.Core.Tests/Http2ConnectionTests.cs
index e183f10523..5b1172e240 100644
--- a/test/Kestrel.Core.Tests/Http2ConnectionTests.cs
+++ b/test/Kestrel.Core.Tests/Http2ConnectionTests.cs
@@ -1065,12 +1065,6 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Tests
         [Fact]
         public async Task DATA_Received_NoStreamWindowSpace_ConnectionError()
         {
-            // I hate doing this, but it avoids exceptions from MemoryPool.Dipose() in debug mode. The problem is since
-            // the stream's ProcessRequestsAsync loop is never awaited by the connection, it's not really possible to
-            // observe when all the blocks are returned. This can be removed after we implement graceful shutdown.
-            Dispose();
-            InitializeConnectionFields(new DiagnosticMemoryPool(KestrelMemoryPool.CreateSlabMemoryPool(), allowLateReturn: true));
-
             // _maxData should be 1/4th of the default initial window size + 1.
             Assert.Equal(Http2PeerSettings.DefaultInitialWindowSize + 1, (uint)_maxData.Length * 4);
 
@@ -1093,12 +1087,6 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Tests
         [Fact]
         public async Task DATA_Received_NoConnectionWindowSpace_ConnectionError()
         {
-            // I hate doing this, but it avoids exceptions from MemoryPool.Dipose() in debug mode. The problem is since
-            // the stream's ProcessRequestsAsync loop is never awaited by the connection, it's not really possible to
-            // observe when all the blocks are returned. This can be removed after we implement graceful shutdown.
-            Dispose();
-            InitializeConnectionFields(new DiagnosticMemoryPool(KestrelMemoryPool.CreateSlabMemoryPool(), allowLateReturn: true));
-
             // _maxData should be 1/4th of the default initial window size + 1.
             Assert.Equal(Http2PeerSettings.DefaultInitialWindowSize + 1, (uint)_maxData.Length * 4);
 
@@ -3287,7 +3275,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.Core.Tests
             _pair.Application.Output.Complete(new ConnectionResetException(string.Empty));
 
             var result = await _pair.Application.Input.ReadAsync();
-            Assert.True(result.IsCompleted);
+            Assert.False(result.IsCompleted);
             Assert.Single(_logger.Messages, m => m.Exception is ConnectionResetException);
         }
 
diff --git a/test/Kestrel.Transport.FunctionalTests/Http2/H2SpecTests.cs b/test/Kestrel.Transport.FunctionalTests/Http2/H2SpecTests.cs
index b5a196c5f2..baca985366 100644
--- a/test/Kestrel.Transport.FunctionalTests/Http2/H2SpecTests.cs
+++ b/test/Kestrel.Transport.FunctionalTests/Http2/H2SpecTests.cs
@@ -27,9 +27,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.FunctionalTests.Http2
         [MemberData(nameof(H2SpecTestCases))]
         public async Task RunIndividualTestCase(H2SpecTestCase testCase)
         {
-            var memoryPoolFactory = new DiagnosticMemoryPoolFactory(allowLateReturn: true);
-
-            var hostBuilder = TransportSelector.GetWebHostBuilder(memoryPoolFactory.Create)
+            var hostBuilder = TransportSelector.GetWebHostBuilder()
                 .UseKestrel(options =>
                 {
                     options.Listen(IPAddress.Loopback, 0, listenOptions =>
@@ -66,7 +64,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.FunctionalTests.Http2
                     {
                         skip = "https://github.com/aspnet/KestrelHttpServer/issues/2154";
                     }
-                    
+
                     dataset.Add(new H2SpecTestCase()
                     {
                         Id = testcase.Item1,
@@ -74,7 +72,7 @@ namespace Microsoft.AspNetCore.Server.Kestrel.FunctionalTests.Http2
                         Https = false,
                         Skip = skip,
                     });
-                    
+
                     dataset.Add(new H2SpecTestCase()
                     {
                         Id = testcase.Item1,