diff --git a/src/time/mono_test.go b/src/time/mono_test.go
index dfb88e792b..794f1d1b1c 100644
--- a/src/time/mono_test.go
+++ b/src/time/mono_test.go
@@ -54,8 +54,8 @@ func TestHasMonotonicClock(t *testing.T) {
 	yes("tm.In(UTC)", tm.In(UTC))
 	yes("tm.Local()", tm.Local())
 	yes("tm.UTC()", tm.UTC())
-	yes("tm.Round(2)", tm.Round(2))
-	yes("tm.Truncate(2)", tm.Truncate(2))
+	no("tm.Round(2)", tm.Round(2))
+	no("tm.Truncate(2)", tm.Truncate(2))
 }
 
 func TestMonotonicAdd(t *testing.T) {
diff --git a/src/time/time.go b/src/time/time.go
index 48aa1eb8f2..5bb7dd961d 100644
--- a/src/time/time.go
+++ b/src/time/time.go
@@ -37,13 +37,12 @@
 // to use this package.
 //
 // The Time returned by time.Now contains a monotonic clock reading.
-// If Time t has a monotonic clock reading, t.Add, t.Round, and
-// t.Truncate add the same duration to both the wall clock and
-// monotonic clock readings to compute the result. Similarly, t.In,
-// t.Local, and t.UTC, which are defined to change only the Time's
+// If Time t has a monotonic clock reading, t.Add adds the same duration to
+// both the wall clock and monotonic clock readings to compute the result.
+// Similarly, t.In, t.Local, and t.UTC, which are defined to change only the Time's
 // Location, pass any monotonic clock reading through unmodified.
-// Because t.AddDate(y, m, d) is a wall time computation, it always
-// strips any monotonic clock reading from its result.
+// Because t.AddDate(y, m, d), t.Round(d), and t.Truncate(d) are wall time
+// computations, they always strip any monotonic clock reading from their results.
 //
 // If Times t and u both contain monotonic clock readings, the operations
 // t.After(u), t.Before(u), t.Equal(u), and t.Sub(u) are carried out
@@ -172,8 +171,7 @@ func (t *Time) addSec(d int64) {
 		}
 		// Wall second now out of range for packed field.
 		// Move to ext.
-		t.ext = t.sec()
-		t.wall &= nsecMask
+		t.stripMono()
 	}
 
 	// TODO: Check for overflow.
@@ -188,6 +186,14 @@ func (t *Time) setLoc(loc *Location) {
 	t.loc = loc
 }
 
+// stripMono strips the monotonic clock reading in t.
+func (t *Time) stripMono() {
+	if t.wall&hasMonotonic != 0 {
+		t.ext = t.sec()
+		t.wall &= nsecMask
+	}
+}
+
 // setMono sets the monotonic clock reading in t.
 // If t cannot hold a monotonic clock reading,
 // because its wall time is too large,
@@ -839,8 +845,7 @@ func (t Time) Add(d Duration) Time {
 		te := t.ext + int64(d)
 		if d < 0 && te > int64(t.ext) || d > 0 && te < int64(t.ext) {
 			// Monotonic clock reading now out of range; degrade to wall-only.
-			t.ext = t.sec()
-			t.wall &= nsecMask
+			t.stripMono()
 		} else {
 			t.ext = te
 		}
@@ -1373,6 +1378,7 @@ func Date(year int, month Month, day, hour, min, sec, nsec int, loc *Location) T
 // time. Thus, Truncate(Hour) may return a time with a non-zero
 // minute, depending on the time's Location.
 func (t Time) Truncate(d Duration) Time {
+	t.stripMono()
 	if d <= 0 {
 		return t
 	}
@@ -1389,6 +1395,7 @@ func (t Time) Truncate(d Duration) Time {
 // time. Thus, Round(Hour) may return a time with a non-zero
 // minute, depending on the time's Location.
 func (t Time) Round(d Duration) Time {
+	t.stripMono()
 	if d <= 0 {
 		return t
 	}