diff --git a/src/main/java/libcore/net/http/HttpTransport.java b/src/main/java/libcore/net/http/HttpTransport.java
index d30734978..dacffb94f 100644
--- a/src/main/java/libcore/net/http/HttpTransport.java
+++ b/src/main/java/libcore/net/http/HttpTransport.java
@@ -211,10 +211,16 @@ final class HttpTransport implements Transport {
             return false;
         }
 
-        // If the headers specify that the connection shouldn't be reused, don't reuse it.
+        // If the request specified that the connection shouldn't be reused,
+        // don't reuse it. This advice doesn't apply to CONNECT requests because
+        // the "Connection: close" header goes the origin server, not the proxy.
         if (httpEngine.requestHeaders.hasConnectionClose()
-                || (httpEngine.responseHeaders != null
-                && httpEngine.responseHeaders.hasConnectionClose())) {
+                && httpEngine.method != HttpEngine.CONNECT) {
+            return false;
+        }
+
+        // If the response specified that the connection shouldn't be reused, don't reuse it.
+        if (httpEngine.responseHeaders != null && httpEngine.responseHeaders.hasConnectionClose()) {
             return false;
         }
 
diff --git a/src/test/java/libcore/net/http/URLConnectionTest.java b/src/test/java/libcore/net/http/URLConnectionTest.java
index ae4abd2b5..723e32788 100644
--- a/src/test/java/libcore/net/http/URLConnectionTest.java
+++ b/src/test/java/libcore/net/http/URLConnectionTest.java
@@ -748,6 +748,26 @@ public final class URLConnectionTest extends TestCase {
         assertContainsNoneMatching(get.getHeaders(), "Proxy\\-Authorization.*");
     }
 
+    // Don't disconnect after building a tunnel with CONNECT
+    // http://code.google.com/p/android/issues/detail?id=37221
+    public void testProxyWithConnectionClose() throws IOException {
+        server.useHttps(sslContext.getSocketFactory(), true);
+        server.enqueue(new MockResponse()
+                .setSocketPolicy(SocketPolicy.UPGRADE_TO_SSL_AT_END)
+                .clearHeaders());
+        server.enqueue(new MockResponse().setBody("this response comes via a proxy"));
+        server.play();
+
+        URL url = new URL("https://android.com/foo");
+        OkHttpsConnection connection = (OkHttpsConnection) openConnection(
+                url, server.toProxyAddress());
+        connection.setRequestProperty("Connection", "close");
+        connection.setSSLSocketFactory(sslContext.getSocketFactory());
+        connection.setHostnameVerifier(new RecordingHostnameVerifier());
+
+        assertContent("this response comes via a proxy", connection);
+    }
+
     public void testDisconnectedConnection() throws IOException {
         server.enqueue(new MockResponse().setBody("ABCDEFGHIJKLMNOPQR"));
         server.play();