diff --git a/composer.json b/composer.json
index cb15665..52a0868 100644
--- a/composer.json
+++ b/composer.json
@@ -29,13 +29,14 @@
         "php": ">=8.1",
         "amphp/amp": "^3",
         "amphp/byte-stream": "^2.1",
-        "amphp/http": "^2.1",
-        "amphp/http-server": "^3.2",
+        "amphp/http": "dev-structured-fields as v2.1.0",
+        "amphp/http-server": "dev-http3 as 3.4",
         "amphp/socket": "^2.2",
         "amphp/websocket": "^2",
         "psr/log": "^1|^2|^3",
         "revolt/event-loop": "^1"
     },
+    "minimum-stability": "dev",
     "require-dev": {
         "amphp/http-client": "^5",
         "amphp/http-server-static-content": "^2",
diff --git a/src/Rfc6455Acceptor.php b/src/Rfc6455Acceptor.php
index 6c0f415..e5d7a5a 100644
--- a/src/Rfc6455Acceptor.php
+++ b/src/Rfc6455Acceptor.php
@@ -21,57 +21,67 @@ public function __construct(private readonly ErrorHandler $errorHandler = new In
 
     public function handleHandshake(Request $request): Response
     {
-        if ($request->getMethod() !== 'GET') {
-            $response = $this->errorHandler->handleError(HttpStatus::METHOD_NOT_ALLOWED, request: $request);
-            $response->setHeader('allow', 'GET');
-            return $response;
-        }
-
-        if ($request->getProtocolVersion() !== '1.1') {
+        if ($request->getProtocolVersion() < '1.1') {
             $response = $this->errorHandler->handleError(HttpStatus::HTTP_VERSION_NOT_SUPPORTED, request: $request);
             $response->setHeader('upgrade', 'websocket');
             return $response;
         }
 
-        if ('' !== $request->getBody()->buffer()) {
-            return $this->errorHandler->handleError(HttpStatus::BAD_REQUEST, request: $request);
-        }
+        $useExtendedConnect = $request->getProtocolVersion() !== "1.1";
 
-        $hasUpgradeWebsocket = false;
-        foreach ($request->getHeaderArray('upgrade') as $value) {
-            if (\strcasecmp($value, 'websocket') === 0) {
-                $hasUpgradeWebsocket = true;
-                break;
-            }
-        }
-        if (!$hasUpgradeWebsocket) {
-            $response = $this->errorHandler->handleError(HttpStatus::UPGRADE_REQUIRED, request: $request);
-            $response->setHeader('upgrade', 'websocket');
+        $requiredMethod = $useExtendedConnect ? "CONNECT" : "GET";
+        if ($request->getMethod() !== $requiredMethod) {
+            $response = $this->errorHandler->handleError(HttpStatus::METHOD_NOT_ALLOWED, request: $request);
+            $response->setHeader('allow', $requiredMethod);
             return $response;
         }
 
-        $hasConnectionUpgrade = false;
-        foreach ($request->getHeaderArray('connection') as $value) {
-            $values = \array_map('trim', \explode(',', $value));
+        if ($useExtendedConnect) {
+            if ($request->getProtocol() !== "websocket") {
+                $reason = 'Bad request: ":protocol: websocket" required';
+                return $this->errorHandler->handleError(HttpStatus::BAD_REQUEST, $reason, $request);
+            }
+        } else {
+            if ('' !== $request->getBody()->buffer()) {
+                return $this->errorHandler->handleError(HttpStatus::BAD_REQUEST, request: $request);
+            }
 
-            foreach ($values as $token) {
-                if (\strcasecmp($token, 'upgrade') === 0) {
-                    $hasConnectionUpgrade = true;
+            $hasUpgradeWebsocket = false;
+            foreach ($request->getHeaderArray('upgrade') as $value) {
+                if (\strcasecmp($value, 'websocket') === 0) {
+                    $hasUpgradeWebsocket = true;
                     break;
                 }
             }
-        }
+            if (!$hasUpgradeWebsocket) {
+                $response = $this->errorHandler->handleError(HttpStatus::UPGRADE_REQUIRED, request: $request);
+                $response->setHeader('upgrade', 'websocket');
+                return $response;
+            }
 
-        if (!$hasConnectionUpgrade) {
-            $reason = 'Bad Request: "Connection: Upgrade" header required';
-            $response = $this->errorHandler->handleError(HttpStatus::UPGRADE_REQUIRED, $reason, $request);
-            $response->setHeader('upgrade', 'websocket');
-            return $response;
-        }
+            $hasConnectionUpgrade = false;
+            foreach ($request->getHeaderArray('connection') as $value) {
+                $values = \array_map('trim', \explode(',', $value));
+
+                foreach ($values as $token) {
+                    if (\strcasecmp($token, 'upgrade') === 0) {
+                        $hasConnectionUpgrade = true;
+                        break;
+                    }
+                }
+            }
+
+            if (!$hasConnectionUpgrade) {
+                $reason = 'Bad Request: "Connection: Upgrade" header required';
+                $response = $this->errorHandler->handleError(HttpStatus::UPGRADE_REQUIRED, $reason, $request);
+                $response->setHeader('upgrade', 'websocket');
+                return $response;
+            }
 
-        if (!$acceptKey = $request->getHeader('sec-websocket-key')) {
-            $reason = 'Bad Request: "Sec-Websocket-Key" header required';
-            return $this->errorHandler->handleError(HttpStatus::BAD_REQUEST, $reason, $request);
+            if (!$acceptKey = $request->getHeader('sec-websocket-key')) {
+                $reason = 'Bad Request: "Sec-Websocket-Key" header required';
+                return $this->errorHandler->handleError(HttpStatus::BAD_REQUEST, $reason, $request);
+            }
         }
 
         if (!\in_array('13', $request->getHeaderArray('sec-websocket-version'), true)) {
@@ -81,6 +91,10 @@ public function handleHandshake(Request $request): Response
             return $response;
         }
 
+        if ($useExtendedConnect) {
+            return new Response;
+        }
+
         return new Response(HttpStatus::SWITCHING_PROTOCOLS, [
             'connection' => 'upgrade',
             'upgrade' => 'websocket',
diff --git a/src/Websocket.php b/src/Websocket.php
index 52b1b10..750d17f 100644
--- a/src/Websocket.php
+++ b/src/Websocket.php
@@ -53,11 +53,21 @@ public function handleRequest(Request $request): Response
     {
         $response = $this->acceptor->handleHandshake($request);
 
-        if ($response->getStatus() !== HttpStatus::SWITCHING_PROTOCOLS) {
-            $response->removeHeader('sec-websocket-accept');
-            $response->setHeader('connection', 'close');
+        if ($request->getProtocolVersion() < 2) {
+            if ($response->getStatus() !== HttpStatus::SWITCHING_PROTOCOLS) {
+                $response->removeHeader('sec-websocket-accept');
+                $response->setHeader('connection', 'close');
 
-            return $response;
+                return $response;
+            }
+        } else {
+            if ($response->getStatus() >= 300 /* not an OK status */) {
+                return $response;
+            }
+            // Avoid having websocket handlers to take care of versions manually
+            if ($response->getStatus() === HttpStatus::SWITCHING_PROTOCOLS) {
+                $response->setStatus(HttpStatus::OK);
+            }
         }
 
         $compressionContext = $this->negotiateCompression($request, $response);