diff --git a/src/session-pool.ts b/src/session-pool.ts
index c404e18c9..47fb8df9a 100644
--- a/src/session-pool.ts
+++ b/src/session-pool.ts
@@ -997,13 +997,20 @@ export class SessionPool extends EventEmitter implements SessionPoolInterface {
       throw new SessionPoolExhaustedError(this._getLeaks());
     }
 
+    let removeOnceCloseListener: Function;
     let removeListener: Function;
 
     // Wait for the requested type of session to become available.
     const availableEvent = type + '-available';
     const promises = [
-      this._onClose.then(() => {
-        throw new GoogleError(errors.Closed);
+      new Promise((_, reject) => {
+        const onceCloseListener = () => reject(new GoogleError(errors.Closed));
+        this.once('close', onceCloseListener);
+        removeOnceCloseListener = this.removeListener.bind(
+          this,
+          'close',
+          onceCloseListener
+        );
       }),
       new Promise(resolve => {
         this.once(availableEvent, resolve);
@@ -1077,6 +1084,7 @@ export class SessionPool extends EventEmitter implements SessionPoolInterface {
       await Promise.race(promises);
     } finally {
       this._waiters[type]--;
+      removeOnceCloseListener!();
       removeListener!();
       removeErrorListener!();
       removeTimeoutListener();