diff --git a/src/Connection/Http1Connection.php b/src/Connection/Http1Connection.php
index 2b0a99c0..fac7f1e9 100644
--- a/src/Connection/Http1Connection.php
+++ b/src/Connection/Http1Connection.php
@@ -320,6 +320,7 @@ private function readResponse(
             while (null !== $chunk = $this->readChunk($timeout)) {
                 parseChunk:
                 $response = $parser->parse($chunk);
+
                 if ($response === null) {
                     if ($this->socket === null) {
                         throw new SocketException('Socket closed prior to response completion');
@@ -377,17 +378,20 @@ private function readResponse(
                     $bodyDeferredCancellation
                 ));
 
+                [$reqTimeout, $explicitTimeout, $priorTimeout] = $this->determineKeepAliveTimeout($response);
+
                 // Read body async
                 EventLoop::queue(function () use (
                     $parser,
                     $request,
-                    $response,
+                    $reqTimeout,
+                    $explicitTimeout,
+                    $priorTimeout,
                     $bodyEmitter,
                     $trailersDeferred,
                     $originalCancellation,
                     $readingCancellation,
                     $bodyCancellation,
-                    $stream,
                     $timeout,
                     &$trailers
                 ) {
@@ -443,7 +447,14 @@ private function readResponse(
                             }
                         }
 
-                        $timeout = $this->determineKeepAliveTimeout($response);
+                        if ($explicitTimeout) {
+                            $this->explicitTimeout = $explicitTimeout;
+                        }
+                        if ($priorTimeout !== null) {
+                            $this->priorTimeout = $priorTimeout;
+                        }
+
+                        $timeout = $reqTimeout;
 
                         if ($timeout > 0 && $parser->getState() !== Http1Parser::BODY_IDENTITY_EOF) {
                             $this->timeoutWatcher = EventLoop::delay($timeout, $this->close(...));
@@ -546,7 +557,8 @@ private function getRemainingTime(): float
         return \max(0, $timestamp - now());
     }
 
-    private function determineKeepAliveTimeout(Response $response): int
+    /** @return list{int, bool, ?int} */
+    private function determineKeepAliveTimeout(Response $response): array
     {
         $request = $response->getRequest();
 
@@ -554,25 +566,21 @@ private function determineKeepAliveTimeout(Response $response): int
         $responseConnHeader = $response->getHeader('connection') ?? '';
 
         if (!\strcasecmp($requestConnHeader, 'close')) {
-            return 0;
+            return [0, false, null];
         }
 
         if ($response->getProtocolVersion() === '1.0') {
-            return 0;
+            return [0, false, null];
         }
 
         if (!\strcasecmp($responseConnHeader, 'close')) {
-            return 0;
+            return [0, false, null];
         }
 
         $params = Http\parseMultipleHeaderFields($response, 'keep-alive')[0] ?? null;
 
         $timeout = (int) ($params['timeout'] ?? $this->priorTimeout);
-        if (isset($params['timeout'])) {
-            $this->explicitTimeout = true;
-        }
-
-        return $this->priorTimeout = \min(\max(0, $timeout), self::MAX_KEEP_ALIVE_TIMEOUT);
+        return [0, isset($params['timeout']), \min(\max(0, $timeout), self::MAX_KEEP_ALIVE_TIMEOUT)];
     }
 
     /**
diff --git a/src/Connection/Internal/Http1Parser.php b/src/Connection/Internal/Http1Parser.php
index 7b8914b3..dc77da27 100644
--- a/src/Connection/Internal/Http1Parser.php
+++ b/src/Connection/Internal/Http1Parser.php
@@ -13,6 +13,8 @@
 use Amp\Http\HttpMessage;
 use Amp\Http\HttpStatus;
 use Amp\Http\InvalidHeaderException;
+use WeakReference;
+
 use function Amp\Http\Client\events;
 use function Amp\Http\mapHeaderPairs;
 
@@ -39,7 +41,8 @@ final class Http1Parser
     public const TRAILERS_START = 4;
     public const TRAILERS = 5;
 
-    private ?Response $response = null;
+    /** @var ?WeakReference<Response> */
+    private ?WeakReference $response = null;
 
     private int $state = self::AWAITING_HEADERS;
 
@@ -110,9 +113,11 @@ public function parse(?string $data = null): ?Response
 
         if (!$this->bodyStarted && \in_array($this->state, [self::BODY_CHUNKS, self::BODY_IDENTITY, self::BODY_IDENTITY_EOF], true)) {
             $this->bodyStarted = true;
-            $response = $this->response;
-            \assert($response !== null);
-            events()->responseBodyStart($this->request, $this->stream, $response);
+            $response = $this->response?->get();
+            if ($response !== null) {
+                events()->responseBodyStart($this->request, $this->stream, $response);
+                unset($response);
+            }
         }
 
         switch ($this->state) {
@@ -185,13 +190,15 @@ public function parse(?string $data = null): ?Response
 
             events()->responseHeaderEnd($this->request, $this->stream, $response);
 
-            return $this->response = $response;
+            $this->response = WeakReference::create($response);
+            return $response;
         }
 
         body_identity:
         {
-            if ($data !== null && $data !== '') {
-                events()->responseBodyProgress($this->request, $this->stream, $this->response);
+            if ($data !== null && $data !== '' && ($r = $this->response->get())) {
+                events()->responseBodyProgress($this->request, $this->stream, $r);
+                unset($r);
             }
 
             $bufferDataSize = \strlen($this->buffer);
@@ -219,8 +226,9 @@ public function parse(?string $data = null): ?Response
 
         body_identity_eof:
         {
-            if ($data !== null && $data !== '') {
-                events()->responseBodyProgress($this->request, $this->stream, $this->response);
+            if ($data !== null && $data !== '' && ($r = $this->response->get())) {
+                events()->responseBodyProgress($this->request, $this->stream, $r);
+                unset($r);
             }
 
             $this->addToBody($this->buffer);
@@ -230,8 +238,9 @@ public function parse(?string $data = null): ?Response
 
         body_chunks:
         {
-            if ($data !== null && $data !== '') {
-                events()->responseBodyProgress($this->request, $this->stream, $this->response);
+            if ($data !== null && $data !== '' && ($r = $this->response->get())) {
+                events()->responseBodyProgress($this->request, $this->stream, $r);
+                unset($r);
             }
 
             if ($this->parseChunkedBody()) {
@@ -272,7 +281,10 @@ public function parse(?string $data = null): ?Response
 
         complete:
         {
-            events()->responseBodyEnd($this->request, $this->stream, $this->response);
+            if ($r = $this->response->get()) {
+                events()->responseBodyEnd($this->request, $this->stream, $r);
+                unset($r);
+            }
 
             $this->complete = true;
 
diff --git a/test/Connection/ConnectionLimitingPoolTest.php b/test/Connection/ConnectionLimitingPoolTest.php
index 669d3d50..070c1fe9 100644
--- a/test/Connection/ConnectionLimitingPoolTest.php
+++ b/test/Connection/ConnectionLimitingPoolTest.php
@@ -39,6 +39,42 @@ public function testSingleConnection(): void
         ]);
     }
 
+    public function testSingleConnectionDoNotUseBody(): void
+    {
+        $client = (new HttpClientBuilder)
+            ->usingPool(ConnectionLimitingPool::byAuthority(1))
+            ->build();
+
+        $this->setMinimumRuntime(2);
+
+        $r1 = new Request('https://httpbin.org/delay/1');
+        $r1->setProtocolVersions(['1.1']);
+        $r2 = new Request('https://httpbin.org/delay/1');
+        $r2->setProtocolVersions(['1.1']);
+        Future\await([
+            async($client->request(...), $r1),
+            async($client->request(...), $r2),
+        ]);
+    }
+
+    public function testSingleConnectionDoNotUseBodyHttp2(): void
+    {
+        $client = (new HttpClientBuilder)
+            ->usingPool(ConnectionLimitingPool::byAuthority(1))
+            ->build();
+
+        $this->setMinimumRuntime(1);
+
+        $r1 = new Request('https://httpbin.org/delay/1');
+        $r1->setProtocolVersions(['2']);
+        $r2 = new Request('https://httpbin.org/delay/1');
+        $r2->setProtocolVersions(['2']);
+        Future\await([
+            async($client->request(...), $r1),
+            async($client->request(...), $r2),
+        ]);
+    }
+
     public function testTwoConnections(): void
     {
         $client = (new HttpClientBuilder)