diff --git a/src/net/net_test.go b/src/net/net_test.go
index a7406740f5..409e1400af 100644
--- a/src/net/net_test.go
+++ b/src/net/net_test.go
@@ -23,50 +23,54 @@ func TestCloseRead(t *testing.T) {
 	case "plan9":
 		t.Skipf("not supported on %s", runtime.GOOS)
 	}
+	t.Parallel()
 
 	for _, network := range []string{"tcp", "unix", "unixpacket"} {
-		if !testableNetwork(network) {
-			t.Logf("skipping %s test", network)
-			continue
-		}
-
-		ln, err := newLocalListener(network)
-		if err != nil {
-			t.Fatal(err)
-		}
-		switch network {
-		case "unix", "unixpacket":
-			defer os.Remove(ln.Addr().String())
-		}
-		defer ln.Close()
-
-		c, err := Dial(ln.Addr().Network(), ln.Addr().String())
-		if err != nil {
-			t.Fatal(err)
-		}
-		switch network {
-		case "unix", "unixpacket":
-			defer os.Remove(c.LocalAddr().String())
-		}
-		defer c.Close()
-
-		switch c := c.(type) {
-		case *TCPConn:
-			err = c.CloseRead()
-		case *UnixConn:
-			err = c.CloseRead()
-		}
-		if err != nil {
-			if perr := parseCloseError(err, true); perr != nil {
-				t.Error(perr)
+		network := network
+		t.Run(network, func(t *testing.T) {
+			if !testableNetwork(network) {
+				t.Skipf("network %s is not testable on the current platform", network)
 			}
-			t.Fatal(err)
-		}
-		var b [1]byte
-		n, err := c.Read(b[:])
-		if n != 0 || err == nil {
-			t.Fatalf("got (%d, %v); want (0, error)", n, err)
-		}
+			t.Parallel()
+
+			ln, err := newLocalListener(network)
+			if err != nil {
+				t.Fatal(err)
+			}
+			switch network {
+			case "unix", "unixpacket":
+				defer os.Remove(ln.Addr().String())
+			}
+			defer ln.Close()
+
+			c, err := Dial(ln.Addr().Network(), ln.Addr().String())
+			if err != nil {
+				t.Fatal(err)
+			}
+			switch network {
+			case "unix", "unixpacket":
+				defer os.Remove(c.LocalAddr().String())
+			}
+			defer c.Close()
+
+			switch c := c.(type) {
+			case *TCPConn:
+				err = c.CloseRead()
+			case *UnixConn:
+				err = c.CloseRead()
+			}
+			if err != nil {
+				if perr := parseCloseError(err, true); perr != nil {
+					t.Error(perr)
+				}
+				t.Fatal(err)
+			}
+			var b [1]byte
+			n, err := c.Read(b[:])
+			if n != 0 || err == nil {
+				t.Fatalf("got (%d, %v); want (0, error)", n, err)
+			}
+		})
 	}
 }
 
@@ -76,212 +80,240 @@ func TestCloseWrite(t *testing.T) {
 		t.Skipf("not supported on %s", runtime.GOOS)
 	}
 
-	handler := func(ls *localServer, ln Listener) {
-		c, err := ln.Accept()
-		if err != nil {
-			t.Error(err)
-			return
-		}
-		defer c.Close()
-
-		var b [1]byte
-		n, err := c.Read(b[:])
-		if n != 0 || err != io.EOF {
-			t.Errorf("got (%d, %v); want (0, io.EOF)", n, err)
-			return
-		}
-		switch c := c.(type) {
-		case *TCPConn:
-			err = c.CloseWrite()
-		case *UnixConn:
-			err = c.CloseWrite()
-		}
-		if err != nil {
-			if perr := parseCloseError(err, true); perr != nil {
-				t.Error(perr)
-			}
-			t.Error(err)
-			return
-		}
-		n, err = c.Write(b[:])
-		if err == nil {
-			t.Errorf("got (%d, %v); want (any, error)", n, err)
-			return
-		}
+	t.Parallel()
+	deadline, _ := t.Deadline()
+	if !deadline.IsZero() {
+		// Leave 10% headroom on the deadline to report errors and clean up.
+		deadline = deadline.Add(-time.Until(deadline) / 10)
 	}
 
 	for _, network := range []string{"tcp", "unix", "unixpacket"} {
-		if !testableNetwork(network) {
-			t.Logf("skipping %s test", network)
-			continue
-		}
-
-		ls, err := newLocalServer(network)
-		if err != nil {
-			t.Fatal(err)
-		}
-		defer ls.teardown()
-		if err := ls.buildup(handler); err != nil {
-			t.Fatal(err)
-		}
-
-		c, err := Dial(ls.Listener.Addr().Network(), ls.Listener.Addr().String())
-		if err != nil {
-			t.Fatal(err)
-		}
-		switch network {
-		case "unix", "unixpacket":
-			defer os.Remove(c.LocalAddr().String())
-		}
-		defer c.Close()
-
-		switch c := c.(type) {
-		case *TCPConn:
-			err = c.CloseWrite()
-		case *UnixConn:
-			err = c.CloseWrite()
-		}
-		if err != nil {
-			if perr := parseCloseError(err, true); perr != nil {
-				t.Error(perr)
+		network := network
+		t.Run(network, func(t *testing.T) {
+			if !testableNetwork(network) {
+				t.Skipf("network %s is not testable on the current platform", network)
 			}
-			t.Fatal(err)
-		}
-		var b [1]byte
-		n, err := c.Read(b[:])
-		if n != 0 || err != io.EOF {
-			t.Fatalf("got (%d, %v); want (0, io.EOF)", n, err)
-		}
-		n, err = c.Write(b[:])
-		if err == nil {
-			t.Fatalf("got (%d, %v); want (any, error)", n, err)
-		}
+			t.Parallel()
+
+			handler := func(ls *localServer, ln Listener) {
+				c, err := ln.Accept()
+				if err != nil {
+					t.Error(err)
+					return
+				}
+				if !deadline.IsZero() {
+					c.SetDeadline(deadline)
+				}
+				defer c.Close()
+
+				var b [1]byte
+				n, err := c.Read(b[:])
+				if n != 0 || err != io.EOF {
+					t.Errorf("got (%d, %v); want (0, io.EOF)", n, err)
+					return
+				}
+				switch c := c.(type) {
+				case *TCPConn:
+					err = c.CloseWrite()
+				case *UnixConn:
+					err = c.CloseWrite()
+				}
+				if err != nil {
+					if perr := parseCloseError(err, true); perr != nil {
+						t.Error(perr)
+					}
+					t.Error(err)
+					return
+				}
+				n, err = c.Write(b[:])
+				if err == nil {
+					t.Errorf("got (%d, %v); want (any, error)", n, err)
+					return
+				}
+			}
+
+			ls, err := newLocalServer(network)
+			if err != nil {
+				t.Fatal(err)
+			}
+			defer ls.teardown()
+			if err := ls.buildup(handler); err != nil {
+				t.Fatal(err)
+			}
+
+			c, err := Dial(ls.Listener.Addr().Network(), ls.Listener.Addr().String())
+			if err != nil {
+				t.Fatal(err)
+			}
+			if !deadline.IsZero() {
+				c.SetDeadline(deadline)
+			}
+			switch network {
+			case "unix", "unixpacket":
+				defer os.Remove(c.LocalAddr().String())
+			}
+			defer c.Close()
+
+			switch c := c.(type) {
+			case *TCPConn:
+				err = c.CloseWrite()
+			case *UnixConn:
+				err = c.CloseWrite()
+			}
+			if err != nil {
+				if perr := parseCloseError(err, true); perr != nil {
+					t.Error(perr)
+				}
+				t.Fatal(err)
+			}
+			var b [1]byte
+			n, err := c.Read(b[:])
+			if n != 0 || err != io.EOF {
+				t.Fatalf("got (%d, %v); want (0, io.EOF)", n, err)
+			}
+			n, err = c.Write(b[:])
+			if err == nil {
+				t.Fatalf("got (%d, %v); want (any, error)", n, err)
+			}
+		})
 	}
 }
 
 func TestConnClose(t *testing.T) {
+	t.Parallel()
 	for _, network := range []string{"tcp", "unix", "unixpacket"} {
-		if !testableNetwork(network) {
-			t.Logf("skipping %s test", network)
-			continue
-		}
-
-		ln, err := newLocalListener(network)
-		if err != nil {
-			t.Fatal(err)
-		}
-		switch network {
-		case "unix", "unixpacket":
-			defer os.Remove(ln.Addr().String())
-		}
-		defer ln.Close()
-
-		c, err := Dial(ln.Addr().Network(), ln.Addr().String())
-		if err != nil {
-			t.Fatal(err)
-		}
-		switch network {
-		case "unix", "unixpacket":
-			defer os.Remove(c.LocalAddr().String())
-		}
-		defer c.Close()
-
-		if err := c.Close(); err != nil {
-			if perr := parseCloseError(err, false); perr != nil {
-				t.Error(perr)
+		network := network
+		t.Run(network, func(t *testing.T) {
+			if !testableNetwork(network) {
+				t.Skipf("network %s is not testable on the current platform", network)
 			}
-			t.Fatal(err)
-		}
-		var b [1]byte
-		n, err := c.Read(b[:])
-		if n != 0 || err == nil {
-			t.Fatalf("got (%d, %v); want (0, error)", n, err)
-		}
+			t.Parallel()
+
+			ln, err := newLocalListener(network)
+			if err != nil {
+				t.Fatal(err)
+			}
+			switch network {
+			case "unix", "unixpacket":
+				defer os.Remove(ln.Addr().String())
+			}
+			defer ln.Close()
+
+			c, err := Dial(ln.Addr().Network(), ln.Addr().String())
+			if err != nil {
+				t.Fatal(err)
+			}
+			switch network {
+			case "unix", "unixpacket":
+				defer os.Remove(c.LocalAddr().String())
+			}
+			defer c.Close()
+
+			if err := c.Close(); err != nil {
+				if perr := parseCloseError(err, false); perr != nil {
+					t.Error(perr)
+				}
+				t.Fatal(err)
+			}
+			var b [1]byte
+			n, err := c.Read(b[:])
+			if n != 0 || err == nil {
+				t.Fatalf("got (%d, %v); want (0, error)", n, err)
+			}
+		})
 	}
 }
 
 func TestListenerClose(t *testing.T) {
+	t.Parallel()
 	for _, network := range []string{"tcp", "unix", "unixpacket"} {
-		if !testableNetwork(network) {
-			t.Logf("skipping %s test", network)
-			continue
-		}
-
-		ln, err := newLocalListener(network)
-		if err != nil {
-			t.Fatal(err)
-		}
-		switch network {
-		case "unix", "unixpacket":
-			defer os.Remove(ln.Addr().String())
-		}
-
-		dst := ln.Addr().String()
-		if err := ln.Close(); err != nil {
-			if perr := parseCloseError(err, false); perr != nil {
-				t.Error(perr)
+		network := network
+		t.Run(network, func(t *testing.T) {
+			if !testableNetwork(network) {
+				t.Skipf("network %s is not testable on the current platform", network)
 			}
-			t.Fatal(err)
-		}
-		c, err := ln.Accept()
-		if err == nil {
-			c.Close()
-			t.Fatal("should fail")
-		}
+			t.Parallel()
 
-		if network == "tcp" {
-			// We will have two TCP FSMs inside the
-			// kernel here. There's no guarantee that a
-			// signal comes from the far end FSM will be
-			// delivered immediately to the near end FSM,
-			// especially on the platforms that allow
-			// multiple consumer threads to pull pending
-			// established connections at the same time by
-			// enabling SO_REUSEPORT option such as Linux,
-			// DragonFly BSD. So we need to give some time
-			// quantum to the kernel.
-			//
-			// Note that net.inet.tcp.reuseport_ext=1 by
-			// default on DragonFly BSD.
-			time.Sleep(time.Millisecond)
+			ln, err := newLocalListener(network)
+			if err != nil {
+				t.Fatal(err)
+			}
+			switch network {
+			case "unix", "unixpacket":
+				defer os.Remove(ln.Addr().String())
+			}
 
-			cc, err := Dial("tcp", dst)
+			dst := ln.Addr().String()
+			if err := ln.Close(); err != nil {
+				if perr := parseCloseError(err, false); perr != nil {
+					t.Error(perr)
+				}
+				t.Fatal(err)
+			}
+			c, err := ln.Accept()
 			if err == nil {
-				t.Error("Dial to closed TCP listener succeeded.")
-				cc.Close()
+				c.Close()
+				t.Fatal("should fail")
 			}
-		}
+
+			if network == "tcp" {
+				// We will have two TCP FSMs inside the
+				// kernel here. There's no guarantee that a
+				// signal comes from the far end FSM will be
+				// delivered immediately to the near end FSM,
+				// especially on the platforms that allow
+				// multiple consumer threads to pull pending
+				// established connections at the same time by
+				// enabling SO_REUSEPORT option such as Linux,
+				// DragonFly BSD. So we need to give some time
+				// quantum to the kernel.
+				//
+				// Note that net.inet.tcp.reuseport_ext=1 by
+				// default on DragonFly BSD.
+				time.Sleep(time.Millisecond)
+
+				cc, err := Dial("tcp", dst)
+				if err == nil {
+					t.Error("Dial to closed TCP listener succeeded.")
+					cc.Close()
+				}
+			}
+		})
 	}
 }
 
 func TestPacketConnClose(t *testing.T) {
+	t.Parallel()
 	for _, network := range []string{"udp", "unixgram"} {
-		if !testableNetwork(network) {
-			t.Logf("skipping %s test", network)
-			continue
-		}
-
-		c, err := newLocalPacketListener(network)
-		if err != nil {
-			t.Fatal(err)
-		}
-		switch network {
-		case "unixgram":
-			defer os.Remove(c.LocalAddr().String())
-		}
-		defer c.Close()
-
-		if err := c.Close(); err != nil {
-			if perr := parseCloseError(err, false); perr != nil {
-				t.Error(perr)
+		network := network
+		t.Run(network, func(t *testing.T) {
+			if !testableNetwork(network) {
+				t.Skipf("network %s is not testable on the current platform", network)
 			}
-			t.Fatal(err)
-		}
-		var b [1]byte
-		n, _, err := c.ReadFrom(b[:])
-		if n != 0 || err == nil {
-			t.Fatalf("got (%d, %v); want (0, error)", n, err)
-		}
+			t.Parallel()
+
+			c, err := newLocalPacketListener(network)
+			if err != nil {
+				t.Fatal(err)
+			}
+			switch network {
+			case "unixgram":
+				defer os.Remove(c.LocalAddr().String())
+			}
+			defer c.Close()
+
+			if err := c.Close(); err != nil {
+				if perr := parseCloseError(err, false); perr != nil {
+					t.Error(perr)
+				}
+				t.Fatal(err)
+			}
+			var b [1]byte
+			n, _, err := c.ReadFrom(b[:])
+			if n != 0 || err == nil {
+				t.Fatalf("got (%d, %v); want (0, error)", n, err)
+			}
+		})
 	}
 }
 
@@ -366,56 +398,60 @@ func TestAcceptIgnoreAbortedConnRequest(t *testing.T) {
 }
 
 func TestZeroByteRead(t *testing.T) {
+	t.Parallel()
 	for _, network := range []string{"tcp", "unix", "unixpacket"} {
-		if !testableNetwork(network) {
-			t.Logf("skipping %s test", network)
-			continue
-		}
-
-		ln, err := newLocalListener(network)
-		if err != nil {
-			t.Fatal(err)
-		}
-		connc := make(chan Conn, 1)
-		go func() {
-			defer ln.Close()
-			c, err := ln.Accept()
-			if err != nil {
-				t.Error(err)
+		network := network
+		t.Run(network, func(t *testing.T) {
+			if !testableNetwork(network) {
+				t.Skipf("network %s is not testable on the current platform", network)
 			}
-			connc <- c // might be nil
-		}()
-		c, err := Dial(network, ln.Addr().String())
-		if err != nil {
-			t.Fatal(err)
-		}
-		defer c.Close()
-		sc := <-connc
-		if sc == nil {
-			continue
-		}
-		defer sc.Close()
+			t.Parallel()
 
-		if runtime.GOOS == "windows" {
-			// A zero byte read on Windows caused a wait for readability first.
-			// Rather than change that behavior, satisfy it in this test.
-			// See Issue 15735.
-			go io.WriteString(sc, "a")
-		}
+			ln, err := newLocalListener(network)
+			if err != nil {
+				t.Fatal(err)
+			}
+			connc := make(chan Conn, 1)
+			go func() {
+				defer ln.Close()
+				c, err := ln.Accept()
+				if err != nil {
+					t.Error(err)
+				}
+				connc <- c // might be nil
+			}()
+			c, err := Dial(network, ln.Addr().String())
+			if err != nil {
+				t.Fatal(err)
+			}
+			defer c.Close()
+			sc := <-connc
+			if sc == nil {
+				return
+			}
+			defer sc.Close()
 
-		n, err := c.Read(nil)
-		if n != 0 || err != nil {
-			t.Errorf("%s: zero byte client read = %v, %v; want 0, nil", network, n, err)
-		}
+			if runtime.GOOS == "windows" {
+				// A zero byte read on Windows caused a wait for readability first.
+				// Rather than change that behavior, satisfy it in this test.
+				// See Issue 15735.
+				go io.WriteString(sc, "a")
+			}
 
-		if runtime.GOOS == "windows" {
-			// Same as comment above.
-			go io.WriteString(c, "a")
-		}
-		n, err = sc.Read(nil)
-		if n != 0 || err != nil {
-			t.Errorf("%s: zero byte server read = %v, %v; want 0, nil", network, n, err)
-		}
+			n, err := c.Read(nil)
+			if n != 0 || err != nil {
+				t.Errorf("%s: zero byte client read = %v, %v; want 0, nil", network, n, err)
+			}
+
+			if runtime.GOOS == "windows" {
+				// Same as comment above.
+				go io.WriteString(c, "a")
+			}
+			n, err = sc.Read(nil)
+			if n != 0 || err != nil {
+				t.Errorf("%s: zero byte server read = %v, %v; want 0, nil", network, n, err)
+			}
+		})
 	}
 }