diff --git a/cmd/tests/cmd_run_test.go b/cmd/tests/cmd_run_test.go
index dbf777000c66..34faec1c229a 100644
--- a/cmd/tests/cmd_run_test.go
+++ b/cmd/tests/cmd_run_test.go
@@ -13,6 +13,7 @@ import (
 	"runtime"
 	"strings"
 	"sync"
+	"sync/atomic"
 	"syscall"
 	"testing"
 	"time"
@@ -2001,28 +2002,25 @@ func TestBadLogOutput(t *testing.T) {
 	}
 }
 
+// HACK: We need this so multiple tests can register differently named modules.
+var uniqueModuleNumber uint64 //nolint:gochecknoglobals
+
 // Tests that the appropriate events are emitted at the appropriate times.
 func TestEventSystemOK(t *testing.T) {
 	t.Parallel()
 
 	ts := NewGlobalTestState(t)
 
-	// HACK: We need to be able to run multiple tests in parallel on the events
-	// module, but since it does event subscription in a sync.Once and the API
-	// addresses need to be different for separate tests, we register separate
-	// modules to workaround it. I experimented with passing the address via
-	// the script, but the sync.Once is still a problem.
-	// Note that this also forbids running these tests with more than -count=1,
-	// unless we dynamically increment the module name... /sigh
-	modules.Register("k6/x/testevents1", events.New(
+	moduleName := fmt.Sprintf("k6/x/testevents-%d", atomic.AddUint64(&uniqueModuleNumber, 1))
+	modules.Register(moduleName, events.New(
 		ts.GlobalState.DefaultFlags.Address, []event.Type{
 			event.Init, event.TestStart, event.IterStart, event.IterEnd,
 			event.TestEnd, event.Exit,
 		}))
 
 	ts.CmdArgs = []string{"k6", "--quiet", "run", "-"}
-	ts.Stdin = bytes.NewBuffer([]byte(`
-		import events from 'k6/x/testevents1';
+	ts.Stdin = bytes.NewBuffer([]byte(fmt.Sprintf(`
+		import events from '%s';
 		import { sleep } from 'k6';
 
 		export let options = {
@@ -2031,7 +2029,7 @@ func TestEventSystemOK(t *testing.T) {
 		}
 
 		export default function () { sleep(1); }
-	`))
+	`, moduleName)))
 
 	cmd.ExecuteWithGlobalState(ts.GlobalState)
 
@@ -2061,15 +2059,16 @@ func TestEventSystemAborted(t *testing.T) {
 
 	ts := NewGlobalTestState(t)
 
-	modules.Register("k6/x/testevents2", events.New(
+	moduleName := fmt.Sprintf("k6/x/testevents-%d", atomic.AddUint64(&uniqueModuleNumber, 1))
+	modules.Register(moduleName, events.New(
 		ts.GlobalState.DefaultFlags.Address, []event.Type{
 			event.Init, event.TestStart, event.TestEnd, event.Exit,
 		}))
 
 	ts.CmdArgs = []string{"k6", "--quiet", "run", "-"}
 	ts.ExpectedExitCode = int(exitcodes.ScriptAborted)
-	ts.Stdin = bytes.NewBuffer([]byte(`
-		import events from 'k6/x/testevents2';
+	ts.Stdin = bytes.NewBuffer([]byte(fmt.Sprintf(`
+		import events from '%s';
 		import { test } from 'k6/execution';
 		import { sleep } from 'k6';
 
@@ -2082,7 +2081,7 @@ func TestEventSystemAborted(t *testing.T) {
 			sleep(1);
 			test.abort('oops!');
 		}
-	`))
+	`, moduleName)))
 
 	cmd.ExecuteWithGlobalState(ts.GlobalState)