diff --git a/src/runtime/race/testdata/mop_test.go b/src/runtime/race/testdata/mop_test.go
index 095ead6c9a..7f95051a8c 100644
--- a/src/runtime/race/testdata/mop_test.go
+++ b/src/runtime/race/testdata/mop_test.go
@@ -335,6 +335,8 @@ func TestRaceRange(t *testing.T) {
 			}
 			done <- true
 		}(i)
+		// Ensure the goroutine runs before we continue the loop.
+		runtime.Gosched()
 	}
 	for i := 0; i < N; i++ {
 		<-done
@@ -1727,13 +1729,16 @@ func TestNoRaceAsFunc4(t *testing.T) {
 }
 
 func TestRaceHeapParam(t *testing.T) {
+	done := make(chan bool)
 	x := func() (x int) {
 		go func() {
 			x = 42
+			done <- true
 		}()
 		return
 	}()
 	_ = x
+	<-done
 }
 
 func TestNoRaceEmptyStruct(t *testing.T) {
diff --git a/src/runtime/race/testdata/rwmutex_test.go b/src/runtime/race/testdata/rwmutex_test.go
index 85cb5df3cb..7ac829d759 100644
--- a/src/runtime/race/testdata/rwmutex_test.go
+++ b/src/runtime/race/testdata/rwmutex_test.go
@@ -54,13 +54,16 @@ func TestNoRaceRWMutex(t *testing.T) {
 func TestRaceRWMutexMultipleReaders(t *testing.T) {
 	var mu sync.RWMutex
 	var x, y int64 = 0, 1
-	ch := make(chan bool, 3)
+	ch := make(chan bool, 4)
 	go func() {
 		mu.Lock()
 		defer mu.Unlock()
 		x = 2
 		ch <- true
 	}()
+	// Use three readers so that no matter what order they're
+	// scheduled in, two will be on the same side of the write
+	// lock above.
 	go func() {
 		mu.RLock()
 		y = x + 1
@@ -73,6 +76,13 @@ func TestRaceRWMutexMultipleReaders(t *testing.T) {
 		mu.RUnlock()
 		ch <- true
 	}()
+	go func() {
+		mu.RLock()
+		y = x + 3
+		mu.RUnlock()
+		ch <- true
+	}()
+	<-ch
 	<-ch
 	<-ch
 	<-ch
@@ -82,7 +92,7 @@ func TestRaceRWMutexMultipleReaders(t *testing.T) {
 func TestNoRaceRWMutexMultipleReaders(t *testing.T) {
 	var mu sync.RWMutex
 	x := int64(0)
-	ch := make(chan bool, 3)
+	ch := make(chan bool, 4)
 	go func() {
 		mu.Lock()
 		defer mu.Unlock()
@@ -103,6 +113,14 @@ func TestNoRaceRWMutexMultipleReaders(t *testing.T) {
 		mu.RUnlock()
 		ch <- true
 	}()
+	go func() {
+		mu.RLock()
+		y := x + 3
+		_ = y
+		mu.RUnlock()
+		ch <- true
+	}()
+	<-ch
 	<-ch
 	<-ch
 	<-ch