diff --git a/src/Connection/ConnectionLimitingPool.php b/src/Connection/ConnectionLimitingPool.php
index 9de3acf0..6beb0f06 100644
--- a/src/Connection/ConnectionLimitingPool.php
+++ b/src/Connection/ConnectionLimitingPool.php
@@ -26,6 +26,9 @@ final class ConnectionLimitingPool implements ConnectionPool
     /** @var Promise[][] */
     private $connections = [];
 
+    /** @var int[] */
+    private $activeRequestCounts = [];
+
     /** @var Deferred[][] */
     private $waiting = [];
 
@@ -112,6 +115,9 @@ public function getStream(Request $request, CancellationToken $cancellation): Pr
             /** @var Stream $stream */
             [$connection, $stream] = yield from $this->getStreamFor($uri, $request, $cancellation);
 
+            $connectionId = \spl_object_id($connection);
+            $this->activeRequestCounts[$connectionId] = ($this->activeRequestCounts[$connectionId] ?? 0) + 1;
+
             return HttpStream::fromStream(
                 $stream,
                 coroutine(function (Request $request, CancellationToken $cancellationToken) use (
@@ -170,6 +176,11 @@ private function getStreamFor(string $uri, Request $request, CancellationToken $
                 $stream = yield $this->getStreamFromConnection($connection, $request);
 
                 if ($stream === null) {
+                    if (!$this->isAdditionalConnectionAllowed($uri) && $this->isConnectionIdle($connection)) {
+                        $connection->close();
+                        break;
+                    }
+
                     continue; // No stream available for the given request.
                 }
 
@@ -281,6 +292,11 @@ private function isAdditionalConnectionAllowed(string $uri): bool
 
     private function onReadyConnection(Connection $connection, string $uri): void
     {
+        $connectionId = \spl_object_id($connection);
+        if (isset($this->activeRequestCounts[$connectionId])) {
+            $this->activeRequestCounts[$connectionId]--;
+        }
+
         if (empty($this->waiting[$uri])) {
             return;
         }
@@ -290,6 +306,18 @@ private function onReadyConnection(Connection $connection, string $uri): void
         $deferred->resolve($connection);
     }
 
+    private function isConnectionIdle(Connection $connection): bool
+    {
+        $connectionId = \spl_object_id($connection);
+
+        \assert(
+            !isset($this->activeRequestCounts[$connectionId])
+            || $this->activeRequestCounts[$connectionId] >= 0
+        );
+
+        return ($this->activeRequestCounts[$connectionId] ?? 0) === 0;
+    }
+
     private function removeWaiting(string $uri, int $deferredId): void
     {
         unset($this->waiting[$uri][$deferredId]);
@@ -300,7 +328,7 @@ private function removeWaiting(string $uri, int $deferredId): void
 
     private function dropConnection(string $uri, int $connectionId): void
     {
-        unset($this->connections[$uri][$connectionId]);
+        unset($this->connections[$uri][$connectionId], $this->activeRequestCounts[$connectionId]);
 
         if (empty($this->connections[$uri])) {
             unset($this->connections[$uri], $this->waitForPriorConnection[$uri]);
diff --git a/src/Connection/Http1Connection.php b/src/Connection/Http1Connection.php
index 75994ada..fa1f312c 100644
--- a/src/Connection/Http1Connection.php
+++ b/src/Connection/Http1Connection.php
@@ -71,7 +71,7 @@ final class Http1Connection implements Connection
     private $timeoutGracePeriod;
 
     /** @var int */
-    private $estimatedClose;
+    private $lastUsedAt;
 
     /** @var bool */
     private $explicitTimeout = false;
@@ -92,7 +92,7 @@ public function __construct(EncryptableSocket $socket, int $timeoutGracePeriod =
         $this->remoteAddress = $socket->getRemoteAddress();
         $this->tlsInfo = $socket->getTlsInfo();
         $this->timeoutGracePeriod = $timeoutGracePeriod;
-        $this->estimatedClose = getCurrentTime() + self::MAX_KEEP_ALIVE_TIMEOUT * 1000;
+        $this->lastUsedAt = getCurrentTime();
     }
 
     public function __destruct()
@@ -157,7 +157,7 @@ public function getStream(Request $request): Promise
     private function free(): Promise
     {
         $this->socket = null;
-        $this->estimatedClose = 0;
+        $this->lastUsedAt = 0;
 
         if ($this->timeoutWatcher !== null) {
             Loop::cancel($this->timeoutWatcher);
@@ -177,12 +177,10 @@ private function free(): Promise
 
     private function hasStreamFor(Request $request): bool
     {
-        $connectionUnlikelyToClose = $this->explicitTimeout && $this->getRemainingTime() > $this->timeoutGracePeriod;
-
         return !$this->busy
             && $this->socket
             && !$this->socket->isClosed()
-            && ($connectionUnlikelyToClose || $request->isIdempotent());
+            && ($this->getRemainingTime() > 0 || $request->isIdempotent());
     }
 
     /** @inheritdoc */
@@ -406,7 +404,6 @@ private function readResponse(
                         if ($timeout > 0 && $parser->getState() !== Http1Parser::BODY_IDENTITY_EOF) {
                             $this->timeoutWatcher = Loop::delay($timeout * 1000, [$this, 'close']);
                             Loop::unreference($this->timeoutWatcher);
-                            $this->estimatedClose = getCurrentTime() + $timeout * 1000;
                         } else {
                             $this->close();
                         }
@@ -482,7 +479,8 @@ private function handleUpgradeResponse(Request $request, Response $response, str
      */
     private function getRemainingTime(): int
     {
-        return \max(0, $this->estimatedClose - getCurrentTime());
+        $timestamp = $this->lastUsedAt + $this->explicitTimeout ? $this->priorTimeout * 1000 : $this->timeoutGracePeriod;
+        return \max(0, $timestamp - getCurrentTime());
     }
 
     private function withCancellation(Promise $promise, CancellationToken $cancellationToken): Promise