diff --git a/src/testing/sub_test.go b/src/testing/sub_test.go
index 8c989714a1c..5a6d51be592 100644
--- a/src/testing/sub_test.go
+++ b/src/testing/sub_test.go
@@ -706,6 +706,55 @@ func TestRacyOutput(t *T) {
 	}
 }
 
+// The late log message did not include the test name.  Issue 29388.
+func TestLogAfterComplete(t *T) {
+	ctx := newTestContext(1, newMatcher(regexp.MatchString, "", ""))
+	var buf bytes.Buffer
+	t1 := &T{
+		common: common{
+			// Use a buffered channel so that tRunner can write
+			// to it although nothing is reading from it.
+			signal: make(chan bool, 1),
+			w:      &buf,
+		},
+		context: ctx,
+	}
+
+	c1 := make(chan bool)
+	c2 := make(chan string)
+	tRunner(t1, func(t *T) {
+		t.Run("TestLateLog", func(t *T) {
+			go func() {
+				defer close(c2)
+				defer func() {
+					p := recover()
+					if p == nil {
+						c2 <- "subtest did not panic"
+						return
+					}
+					s, ok := p.(string)
+					if !ok {
+						c2 <- fmt.Sprintf("subtest panic with unexpected value %v", p)
+						return
+					}
+					const want = "Log in goroutine after TestLateLog has completed"
+					if !strings.Contains(s, want) {
+						c2 <- fmt.Sprintf("subtest panic %q does not contain %q", s, want)
+					}
+				}()
+
+				<-c1
+				t.Log("log after test")
+			}()
+		})
+	})
+	close(c1)
+
+	if s := <-c2; s != "" {
+		t.Error(s)
+	}
+}
+
 func TestBenchmark(t *T) {
 	res := Benchmark(func(b *B) {
 		for i := 0; i < 5; i++ {
diff --git a/src/testing/testing.go b/src/testing/testing.go
index 0ac51b6fe51..3068630e8a9 100644
--- a/src/testing/testing.go
+++ b/src/testing/testing.go
@@ -618,17 +618,20 @@ func (c *common) log(s string) {
 func (c *common) logDepth(s string, depth int) {
 	c.mu.Lock()
 	defer c.mu.Unlock()
-	// If this test has already finished try and log this message with our parent
-	// with this test name tagged so we know where it came from.
-	// If we don't have a parent panic.
-	if c.done {
-		if c.parent != nil {
-			c.parent.logDepth(s, depth+1)
-		} else {
-			panic("Log in goroutine after " + c.name + " has completed")
-		}
-	} else {
+	if !c.done {
 		c.output = append(c.output, c.decorate(s, depth+1)...)
+	} else {
+		// This test has already finished. Try and log this message
+		// with our parent. If we don't have a parent, panic.
+		for parent := c.parent; parent != nil; parent = parent.parent {
+			parent.mu.Lock()
+			defer parent.mu.Unlock()
+			if !parent.done {
+				parent.output = append(parent.output, parent.decorate(s, depth+1)...)
+				return
+			}
+		}
+		panic("Log in goroutine after " + c.name + " has completed")
 	}
 }