diff --git a/lib/adapters/http.js b/lib/adapters/http.js
index ea69ff2..5326dd0 100755
--- a/lib/adapters/http.js
+++ b/lib/adapters/http.js
@@ -87,7 +87,15 @@ class Http2Sessions {
 
     const session = connect(authority, options);
 
-    session.once('close', () => {
+    let removed;
+
+    const removeSession = () => {
+      if (removed) {
+        return;
+      }
+
+      removed = true;
+
       let entries = authoritySessions, len = entries.length, i = len;
 
       while (i--) {
@@ -99,9 +107,41 @@ class Http2Sessions {
           }
         }
       }
-    });
+    };
 
-    Http2Sessions.setTimeout(session, options.sessionTimeout);
+    const originalRequestFn = session.request;
+
+    const {sessionTimeout} = options;
+
+    if(sessionTimeout != null) {
+
+      let timer;
+      let streamsCount = 0;
+
+      session.request = function () {
+        const stream = originalRequestFn.apply(this, arguments);
+
+        streamsCount++;
+
+        if (timer) {
+          clearTimeout(timer);
+          timer = null;
+        }
+
+        stream.once('close', () => {
+          if (!--streamsCount) {
+            timer = setTimeout(() => {
+              timer = null;
+              removeSession();
+            }, sessionTimeout);
+          }
+        });
+
+        return stream;
+      }
+    }
+
+    session.once('close', removeSession);
 
     let entries = this.sessions[authority], entry = [
       session,
@@ -112,12 +152,6 @@ class Http2Sessions {
 
     return session;
   }
-
-  static setTimeout(session, timeout = 1000) {
-    session && session.setTimeout(timeout, () => {
-      session.close();
-    });
-  }
 }
 
 const http2Sessions = new Http2Sessions();
@@ -284,10 +318,12 @@ export default isHttpAdapterSupported && function httpAdapter(config) {
     let rejected = false;
     let req;
 
-    httpVersion = Number(httpVersion);
+    httpVersion = +httpVersion;
+
     if (Number.isNaN(httpVersion)) {
       throw TypeError(`Invalid protocol version: '${config.httpVersion}' is not a number`);
     }
+
     if (httpVersion !== 1 && httpVersion !== 2) {
       throw TypeError(`Unsupported protocol version '${httpVersion}'`);
     }
diff --git a/test/unit/adapters/http.js b/test/unit/adapters/http.js
index 2f63bbf..7d0cf18 100644
--- a/test/unit/adapters/http.js
+++ b/test/unit/adapters/http.js
@@ -2423,7 +2423,7 @@ describe('supports http with nodejs', function () {
     });
 
     it('should support request cancellation', async function (){
-      if (typeof AbortSignal !== 'function') {
+      if (typeof AbortSignal !== 'function' || !AbortSignal.timeout) {
         this.skip();
       }
 
@@ -2525,13 +2525,17 @@ describe('supports http with nodejs', function () {
 
       it("should use different sessions for different authorities", async() => {
         server = await startHTTPServer((req, res) => {
-          setTimeout(() => res.end('OK'), 1000);
+          setTimeout(() => {
+            res.end('OK');
+          }, 2000);
         }, {
           useHTTP2: true
         });
 
         server2 = await startHTTPServer((req, res) => {
-          setTimeout(() => res.end('OK'), 1000);
+          setTimeout(() => {
+            res.end('OK');
+          }, 2000);
         }, {
           useHTTP2: true,
           port: SERVER_PORT2
@@ -2559,7 +2563,9 @@ describe('supports http with nodejs', function () {
 
       it("should use different sessions for requests with different http2Options set", async() => {
         server = await startHTTPServer((req, res) => {
-          setTimeout(() => res.end('OK'), 1000);
+          setTimeout(() => {
+            res.end('OK')
+          }, 1000);
         }, {
           useHTTP2: true
         });
@@ -2639,6 +2645,8 @@ describe('supports http with nodejs', function () {
           }
         });
 
+        const data1 = await getStream(response1.data);
+
         await setTimeoutAsync(5000);
 
         const response2 = await http2Axios.get(LOCAL_SERVER_URL, {
@@ -2648,15 +2656,12 @@ describe('supports http with nodejs', function () {
           }
         });
 
+        const data2 = await getStream(response2.data);
+
         assert.notStrictEqual(response1.data.session, response2.data.session);
 
-        assert.deepStrictEqual(
-          await Promise.all([
-            getStream(response1.data),
-            getStream(response2.data)
-          ]),
-          ['OK', 'OK']
-        );
+        assert.strictEqual(data1, 'OK');
+        assert.strictEqual(data2, 'OK');
       });
     });
   });