diff --git a/Sources/AsyncHTTPClient/ConnectionPool/State Machine/HTTPConnectionPool+HTTP2StateMachine.swift b/Sources/AsyncHTTPClient/ConnectionPool/State Machine/HTTPConnectionPool+HTTP2StateMachine.swift
index 003de4223..9964ccd05 100644
--- a/Sources/AsyncHTTPClient/ConnectionPool/State Machine/HTTPConnectionPool+HTTP2StateMachine.swift	
+++ b/Sources/AsyncHTTPClient/ConnectionPool/State Machine/HTTPConnectionPool+HTTP2StateMachine.swift	
@@ -404,25 +404,34 @@ extension HTTPConnectionPool {
         }
 
         mutating func failedToCreateNewConnection(_ error: Error, connectionID: Connection.ID) -> Action {
-            // TODO: switch over state https://github.com/swift-server/async-http-client/issues/638
             self.failedConsecutiveConnectionAttempts += 1
             self.lastConnectFailure = error
 
-            guard self.retryConnectionEstablishment else {
-                guard let (index, _) = self.connections.failConnection(connectionID) else {
-                    preconditionFailure("A connection attempt failed, that the state machine knows nothing about. Somewhere state was lost.")
+            switch self.lifecycleState {
+            case .running:
+                guard self.retryConnectionEstablishment else {
+                    guard let (index, _) = self.connections.failConnection(connectionID) else {
+                        preconditionFailure("A connection attempt failed, that the state machine knows nothing about. Somewhere state was lost.")
+                    }
+                    self.connections.removeConnection(at: index)
+
+                    return .init(
+                        request: self.failAllRequests(reason: error),
+                        connection: .none
+                    )
                 }
-                self.connections.removeConnection(at: index)
 
-                return .init(
-                    request: self.failAllRequests(reason: error),
-                    connection: .none
-                )
+                let eventLoop = self.connections.backoffNextConnectionAttempt(connectionID)
+                let backoff = calculateBackoff(failedAttempt: self.failedConsecutiveConnectionAttempts)
+                return .init(request: .none, connection: .scheduleBackoffTimer(connectionID, backoff: backoff, on: eventLoop))
+            case .shuttingDown:
+                guard let (index, context) = self.connections.failConnection(connectionID) else {
+                    preconditionFailure("A connection attempt failed, that the state machine knows nothing about. Somewhere state was lost.")
+                }
+                return self.nextActionForFailedConnection(at: index, on: context.eventLoop)
+            case .shutDown:
+                preconditionFailure("If the pool is already shutdown, all connections must have been torn down.")
             }
-
-            let eventLoop = self.connections.backoffNextConnectionAttempt(connectionID)
-            let backoff = calculateBackoff(failedAttempt: self.failedConsecutiveConnectionAttempts)
-            return .init(request: .none, connection: .scheduleBackoffTimer(connectionID, backoff: backoff, on: eventLoop))
         }
 
         mutating func waitingForConnectivity(_ error: Error, connectionID: Connection.ID) -> Action {
diff --git a/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests+XCTest.swift b/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests+XCTest.swift
index 95ea8c580..12b031cc0 100644
--- a/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests+XCTest.swift
+++ b/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests+XCTest.swift
@@ -27,6 +27,7 @@ extension HTTPConnectionPool_HTTP2StateMachineTests {
         return [
             ("testCreatingOfConnection", testCreatingOfConnection),
             ("testConnectionFailureBackoff", testConnectionFailureBackoff),
+            ("testConnectionFailureWhileShuttingDown", testConnectionFailureWhileShuttingDown),
             ("testConnectionFailureWithoutRetry", testConnectionFailureWithoutRetry),
             ("testCancelRequestWorks", testCancelRequestWorks),
             ("testExecuteOnShuttingDownPool", testExecuteOnShuttingDownPool),
diff --git a/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests.swift b/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests.swift
index bf1ef4a98..10fad7bd6 100644
--- a/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests.swift
+++ b/Tests/AsyncHTTPClientTests/HTTPConnectionPool+HTTP2StateMachineTests.swift
@@ -194,6 +194,44 @@ class HTTPConnectionPool_HTTP2StateMachineTests: XCTestCase {
         XCTAssertEqual(state.connectionCreationBackoffDone(newConnectionID), .none)
     }
 
+    func testConnectionFailureWhileShuttingDown() {
+        struct SomeError: Error, Equatable {}
+        let elg = EmbeddedEventLoopGroup(loops: 4)
+        defer { XCTAssertNoThrow(try elg.syncShutdownGracefully()) }
+
+        var state = HTTPConnectionPool.HTTP2StateMachine(
+            idGenerator: .init(),
+            retryConnectionEstablishment: false,
+            lifecycleState: .running
+        )
+
+        let mockRequest = MockHTTPRequest(eventLoop: elg.next())
+        let request = HTTPConnectionPool.Request(mockRequest)
+
+        let action = state.executeRequest(request)
+        XCTAssertEqual(.scheduleRequestTimeout(for: request, on: mockRequest.eventLoop), action.request)
+
+        // 1. connection attempt
+        guard case .createConnection(let connectionID, on: let connectionEL) = action.connection else {
+            return XCTFail("Unexpected connection action: \(action.connection)")
+        }
+        XCTAssert(connectionEL === mockRequest.eventLoop) // XCTAssertIdentical not available on Linux
+
+        // 2. initialise shutdown
+        let shutdownAction = state.shutdown()
+        XCTAssertEqual(shutdownAction.connection, .cleanupConnections(.init(), isShutdown: .no))
+        guard case .failRequestsAndCancelTimeouts(let requestsToFail, let requestError) = shutdownAction.request else {
+            return XCTFail("Unexpected request action: \(action.request)")
+        }
+        XCTAssertEqualTypeAndValue(requestError, HTTPClientError.cancelled)
+        XCTAssertEqualTypeAndValue(requestsToFail, [request])
+
+        // 3. connection attempt fails
+        let failedConnectAction = state.failedToCreateNewConnection(SomeError(), connectionID: connectionID)
+        XCTAssertEqual(failedConnectAction.request, .none)
+        XCTAssertEqual(failedConnectAction.connection, .cleanupConnections(.init(), isShutdown: .yes(unclean: true)))
+    }
+
     func testConnectionFailureWithoutRetry() {
         struct SomeError: Error, Equatable {}
         let elg = EmbeddedEventLoopGroup(loops: 4)