diff --git a/test/parallel/test-net-better-error-messages-port-hostname.js b/test/parallel/test-net-better-error-messages-port-hostname.js
index 14f84eb15b1..04974908c91 100644
--- a/test/parallel/test-net-better-error-messages-port-hostname.js
+++ b/test/parallel/test-net-better-error-messages-port-hostname.js
@@ -3,12 +3,13 @@ const common = require('../common');
 const net = require('net');
 const assert = require('assert');
 
-const c = net.createConnection(common.PORT, '***');
+// Using port 0 as hostname used is already invalid.
+const c = net.createConnection(0, '***');
 
 c.on('connect', common.mustNotCall());
 
 c.on('error', common.mustCall(function(e) {
   assert.strictEqual(e.code, 'ENOTFOUND');
-  assert.strictEqual(e.port, common.PORT);
+  assert.strictEqual(e.port, 0);
   assert.strictEqual(e.hostname, '***');
 }));
diff --git a/test/parallel/test-net-connect-handle-econnrefused.js b/test/parallel/test-net-connect-handle-econnrefused.js
index 080c60b2d2e..569aded7bf5 100644
--- a/test/parallel/test-net-connect-handle-econnrefused.js
+++ b/test/parallel/test-net-connect-handle-econnrefused.js
@@ -24,13 +24,14 @@ const common = require('../common');
 const net = require('net');
 const assert = require('assert');
 
-
-// Hopefully nothing is running on common.PORT
-const c = net.createConnection(common.PORT);
+const server = net.createServer();
+server.listen(0);
+const port = server.address().port;
+const c = net.createConnection(port);
 
 c.on('connect', common.mustNotCall());
 
-c.on('error', common.mustCall(function(e) {
-  console.error('couldn\'t connect.');
+c.on('error', common.mustCall((e) => {
   assert.strictEqual('ECONNREFUSED', e.code);
 }));
+server.close();
diff --git a/test/parallel/test-net-connect-immediate-destroy.js b/test/parallel/test-net-connect-immediate-destroy.js
index 9a029b5d605..3ca58c356b4 100644
--- a/test/parallel/test-net-connect-immediate-destroy.js
+++ b/test/parallel/test-net-connect-immediate-destroy.js
@@ -2,7 +2,10 @@
 const common = require('../common');
 const net = require('net');
 
-const socket = net.connect(common.PORT, common.localhostIPv4,
-                           common.mustNotCall());
+const server = net.createServer();
+server.listen(0);
+const port = server.address().port;
+const socket = net.connect(port, common.localhostIPv4, common.mustNotCall());
 socket.on('error', common.mustNotCall());
+server.close();
 socket.destroy();
diff --git a/test/parallel/test-net-connect-immediate-finish.js b/test/parallel/test-net-connect-immediate-finish.js
index 340faffcb69..209b90d71d0 100644
--- a/test/parallel/test-net-connect-immediate-finish.js
+++ b/test/parallel/test-net-connect-immediate-finish.js
@@ -26,7 +26,7 @@ const net = require('net');
 
 const client = net.connect({host: '***', port: common.PORT});
 
-client.once('error', common.mustCall(function(err) {
+client.once('error', common.mustCall((err) => {
   assert(err);
   assert.strictEqual(err.code, err.errno);
   assert.strictEqual(err.code, 'ENOTFOUND');
diff --git a/test/parallel/test-net-connect-local-error.js b/test/parallel/test-net-connect-local-error.js
index f23245ac93a..e656b6cb2ac 100644
--- a/test/parallel/test-net-connect-local-error.js
+++ b/test/parallel/test-net-connect-local-error.js
@@ -3,17 +3,20 @@ const common = require('../common');
 const assert = require('assert');
 const net = require('net');
 
+const server = net.createServer();
+server.listen(0);
+const port = server.address().port;
 const client = net.connect({
-  port: common.PORT + 1,
-  localPort: common.PORT,
+  port: port + 1,
+  localPort: port,
   localAddress: common.localhostIPv4
 });
 
 client.on('error', common.mustCall(function onError(err) {
   assert.strictEqual(
     err.localPort,
-    common.PORT,
-    `${err.localPort} !== ${common.PORT} in ${err}`
+    port,
+    `${err.localPort} !== ${port} in ${err}`
   );
   assert.strictEqual(
     err.localAddress,
@@ -21,3 +24,4 @@ client.on('error', common.mustCall(function onError(err) {
     `${err.localAddress} !== ${common.localhostIPv4} in ${err}`
   );
 }));
+server.close();
diff --git a/test/parallel/test-net-localerror.js b/test/parallel/test-net-localerror.js
index 03f8e99c5dc..845983843d8 100644
--- a/test/parallel/test-net-localerror.js
+++ b/test/parallel/test-net-localerror.js
@@ -20,24 +20,25 @@
 // USE OR OTHER DEALINGS IN THE SOFTWARE.
 
 'use strict';
-const common = require('../common');
+require('../common');
 const assert = require('assert');
 const net = require('net');
 
+// Using port 0 as localPort / localAddress is already invalid.
 connect({
   host: 'localhost',
-  port: common.PORT,
+  port: 0,
   localPort: 'foobar',
 }, /^TypeError: "localPort" option should be a number: foobar$/);
 
 connect({
   host: 'localhost',
-  port: common.PORT,
+  port: 0,
   localAddress: 'foobar',
 }, /^TypeError: "localAddress" option must be a valid IP: foobar$/);
 
 function connect(opts, msg) {
-  assert.throws(function() {
+  assert.throws(() => {
     net.connect(opts);
   }, msg);
 }
diff --git a/test/parallel/test-net-options-lookup.js b/test/parallel/test-net-options-lookup.js
index 3559d84e234..c61f338b701 100644
--- a/test/parallel/test-net-options-lookup.js
+++ b/test/parallel/test-net-options-lookup.js
@@ -7,14 +7,15 @@ const expectedError = /^TypeError: "lookup" option should be a function$/;
 
 ['foobar', 1, {}, []].forEach((input) => connectThrows(input));
 
+// Using port 0 as lookup is emitted before connecting.
 function connectThrows(input) {
   const opts = {
     host: 'localhost',
-    port: common.PORT,
+    port: 0,
     lookup: input
   };
 
-  assert.throws(function() {
+  assert.throws(() => {
     net.connect(opts);
   }, expectedError);
 }
@@ -24,11 +25,11 @@ connectDoesNotThrow(common.noop);
 function connectDoesNotThrow(input) {
   const opts = {
     host: 'localhost',
-    port: common.PORT,
+    port: 0,
     lookup: input
   };
 
-  assert.doesNotThrow(function() {
+  assert.doesNotThrow(() => {
     net.connect(opts);
   });
 }
diff --git a/test/parallel/test-net-socket-destroy-twice.js b/test/parallel/test-net-socket-destroy-twice.js
index dacb91adf27..1029d7b2980 100644
--- a/test/parallel/test-net-socket-destroy-twice.js
+++ b/test/parallel/test-net-socket-destroy-twice.js
@@ -23,10 +23,14 @@
 const common = require('../common');
 const net = require('net');
 
-const conn = net.createConnection(common.PORT);
+const server = net.createServer();
+server.listen(0);
+const port = server.address().port;
+const conn = net.createConnection(port);
 
-conn.on('error', common.mustCall(function() {
+conn.on('error', common.mustCall(() => {
   conn.destroy();
 }));
 
 conn.on('close', common.mustCall());
+server.close();
diff --git a/test/parallel/test-net-better-error-messages-port.js b/test/sequential/test-net-better-error-messages-port.js
similarity index 100%
rename from test/parallel/test-net-better-error-messages-port.js
rename to test/sequential/test-net-better-error-messages-port.js
diff --git a/test/parallel/test-net-listen-shared-ports.js b/test/sequential/test-net-listen-shared-ports.js
similarity index 100%
rename from test/parallel/test-net-listen-shared-ports.js
rename to test/sequential/test-net-listen-shared-ports.js