diff --git a/test/async-hooks/test-graph.tcp.js b/test/async-hooks/test-graph.tcp.js
index c2458ef1def769..c2253486ee651e 100644
--- a/test/async-hooks/test-graph.tcp.js
+++ b/test/async-hooks/test-graph.tcp.js
@@ -15,7 +15,7 @@ const server = net
   .createServer(common.mustCall(onconnection))
   .on('listening', common.mustCall(onlistening));
 
-server.listen(common.PORT);
+server.listen(0);
 
 net.connect({ port: server.address().port, host: '::1' },
             common.mustCall(onconnected));
diff --git a/test/async-hooks/test-graph.tls-write.js b/test/async-hooks/test-graph.tls-write.js
index 0c725d153d731b..26fe1ce41e955c 100644
--- a/test/async-hooks/test-graph.tls-write.js
+++ b/test/async-hooks/test-graph.tls-write.js
@@ -25,14 +25,14 @@ const server = tls
   })
   .on('listening', common.mustCall(onlistening))
   .on('secureConnection', common.mustCall(onsecureConnection))
-  .listen(common.PORT);
+  .listen(0);
 
 function onlistening() {
   //
   // Creating client and connecting it to server
   //
   tls
-    .connect(common.PORT, { rejectUnauthorized: false })
+    .connect(server.address().port, { rejectUnauthorized: false })
     .on('secureConnect', common.mustCall(onsecureConnect));
 }
 
diff --git a/test/async-hooks/test-tcpwrap.js b/test/async-hooks/test-tcpwrap.js
index e7d879caf70551..f3100aba0f0aaa 100644
--- a/test/async-hooks/test-tcpwrap.js
+++ b/test/async-hooks/test-tcpwrap.js
@@ -24,7 +24,7 @@ const server = net
 
 // Calling server.listen creates a TCPWRAP synchronously
 {
-  server.listen(common.PORT);
+  server.listen(0);
   const tcpsservers = hooks.activitiesOfTypes('TCPSERVERWRAP');
   const tcpconnects = hooks.activitiesOfTypes('TCPCONNECTWRAP');
   assert.strictEqual(tcpsservers.length, 1);
diff --git a/test/async-hooks/test-writewrap.js b/test/async-hooks/test-writewrap.js
index 65f7b6175fb63a..d349f635665ddd 100644
--- a/test/async-hooks/test-writewrap.js
+++ b/test/async-hooks/test-writewrap.js
@@ -23,7 +23,7 @@ const server = tls
   })
   .on('listening', common.mustCall(onlistening))
   .on('secureConnection', common.mustCall(onsecureConnection))
-  .listen(common.PORT);
+  .listen(0);
 
 assert.strictEqual(hooks.activitiesOfTypes('WRITEWRAP').length, 0);
 
@@ -33,7 +33,7 @@ function onlistening() {
   // Creating client and connecting it to server
   //
   tls
-    .connect(common.PORT, { rejectUnauthorized: false })
+    .connect(server.address().port, { rejectUnauthorized: false })
     .on('secureConnect', common.mustCall(onsecureConnect));
 
   assert.strictEqual(hooks.activitiesOfTypes('WRITEWRAP').length, 0);
diff --git a/test/parallel/test-net-connect-immediate-finish.js b/test/parallel/test-net-connect-immediate-finish.js
index 9adf8c31128b00..27d988ab5af45f 100644
--- a/test/parallel/test-net-connect-immediate-finish.js
+++ b/test/parallel/test-net-connect-immediate-finish.js
@@ -38,9 +38,9 @@ const {
 
 const client = net.connect({
   host: addresses.INVALID_HOST,
-  port: common.PORT,
+  port: 80, // port number doesn't matter because host name is invalid
   lookup: common.mustCall(errorLookupMock())
-});
+}, common.mustNotCall());
 
 client.once('error', common.mustCall((err) => {
   assert(err);
diff --git a/test/parallel/test-tls-connect.js b/test/sequential/test-tls-connect.js
similarity index 100%
rename from test/parallel/test-tls-connect.js
rename to test/sequential/test-tls-connect.js
diff --git a/test/parallel/test-tls-lookup.js b/test/sequential/test-tls-lookup.js
similarity index 100%
rename from test/parallel/test-tls-lookup.js
rename to test/sequential/test-tls-lookup.js