diff --git a/utils/rate_test.go b/utils/rate_test.go
index 961234c00..c4a5dca39 100644
--- a/utils/rate_test.go
+++ b/utils/rate_test.go
@@ -270,7 +270,6 @@ func (r *runnerImpl) goWait(fn func()) {
 }
 
 func TestRateLimiter(t *testing.T) {
-	t.Parallel()
 	runTest(t, func(r testRunner) {
 		rl := r.createLimiter(100, WithoutSlack)
 
@@ -288,7 +287,6 @@ func TestRateLimiter(t *testing.T) {
 
 func TestDelayedRateLimiter(t *testing.T) {
 	t.Skip(UnstableTest)
-	t.Parallel()
 	runTest(t, func(r testRunner) {
 		slow := r.createLimiter(10, WithoutSlack)
 		fast := r.createLimiter(100, WithoutSlack)
@@ -307,7 +305,6 @@ func TestDelayedRateLimiter(t *testing.T) {
 }
 
 func TestPer(t *testing.T) {
-	t.Parallel()
 	runTest(t, func(r testRunner) {
 		rl := r.createLimiter(7, WithoutSlack, Per(time.Minute))
 
@@ -322,7 +319,6 @@ func TestPer(t *testing.T) {
 
 // TestInitial verifies that the initial sequence is scheduled as expected.
 func TestInitial(t *testing.T) {
-	t.Parallel()
 	tests := []struct {
 		msg  string
 		opts []Option
@@ -339,27 +335,25 @@ func TestInitial(t *testing.T) {
 	for _, tt := range tests {
 		t.Run(tt.msg, func(t *testing.T) {
 			runTest(t, func(r testRunner) {
+				perRequest := 100 * time.Millisecond
 				rl := r.createLimiter(10, tt.opts...)
 
 				var (
 					clk  = r.getClock()
 					prev = clk.Now()
 
-					results = make(chan time.Time)
+					results = make(chan time.Time, 3)
 					have    []time.Duration
-					startWg sync.WaitGroup
 				)
-				startWg.Add(3)
 
-				for i := 0; i < 3; i++ {
-					go func() {
-						startWg.Done()
-						results <- rl.Take()
-					}()
-				}
+				results <- rl.Take()
+				clk.Add(perRequest)
+
+				results <- rl.Take()
+				clk.Add(perRequest)
 
-				startWg.Wait()
-				clk.Add(time.Second)
+				results <- rl.Take()
+				clk.Add(perRequest)
 
 				for i := 0; i < 3; i++ {
 					ts := <-results
@@ -370,8 +364,8 @@ func TestInitial(t *testing.T) {
 				assert.Equal(t,
 					[]time.Duration{
 						0,
-						time.Millisecond * 100,
-						time.Millisecond * 100,
+						perRequest,
+						perRequest,
 					},
 					have,
 					"bad timestamps for inital takes",
@@ -382,7 +376,6 @@ func TestInitial(t *testing.T) {
 }
 
 func TestMaxSlack(t *testing.T) {
-	t.Parallel()
 	runTest(t, func(r testRunner) {
 		rl := r.createLimiter(1, WithSlack(1))
 
@@ -398,7 +391,6 @@ func TestMaxSlack(t *testing.T) {
 }
 
 func TestSlack(t *testing.T) {
-	t.Parallel()
 	// To simulate slack, we combine two limiters.
 	// - First, we start a single goroutine with both of them,
 	//   during this time the slow limiter will dominate,