diff --git a/lib/cluster.go b/lib/cluster.go
index 5df39251d8..a95232c573 100644
--- a/lib/cluster.go
+++ b/lib/cluster.go
@@ -10,12 +10,32 @@ import (
 // servicing Consul TTL Checks in advance of the TTL.
 func DurationMinusBuffer(intv time.Duration, buffer time.Duration, jitter int64) time.Duration {
 	d := intv - buffer
-	d -= RandomStagger(time.Duration(int64(d) / jitter))
+	if jitter == 0 {
+		d -= RandomStagger(d)
+	} else {
+		d -= RandomStagger(time.Duration(int64(d) / jitter))
+	}
 	return d
 }
 
+// DurationMinusBufferDomain returns the domain of valid durations from a
+// call to DurationMinusBuffer.  This function is used to check user
+// specified input values to DurationMinusBuffer.
+func DurationMinusBufferDomain(intv time.Duration, buffer time.Duration, jitter int64) (min time.Duration, max time.Duration) {
+	max = intv - buffer
+	if jitter == 0 {
+		min = max
+	} else {
+		min = max - time.Duration(int64(max)/jitter)
+	}
+	return min, max
+}
+
 // Returns a random stagger interval between 0 and the duration
 func RandomStagger(intv time.Duration) time.Duration {
+	if intv == 0 {
+		return 0
+	}
 	return time.Duration(uint64(rand.Int63()) % uint64(intv))
 }
 
diff --git a/lib/cluster_test.go b/lib/cluster_test.go
index acd862f6f1..6747a9698a 100644
--- a/lib/cluster_test.go
+++ b/lib/cluster_test.go
@@ -6,17 +6,123 @@ import (
 )
 
 func TestDurationMinusBuffer(t *testing.T) {
-	const (
-		buffer = 10 * time.Second
-		jitter = 16
-	)
-	intv := 1 * time.Minute
-	minValue := (intv - buffer) - ((intv - buffer) / jitter)
-	maxValue := intv - buffer
-	for i := 0; i < 10; i++ {
-		d := DurationMinusBuffer(intv, buffer, jitter)
-		if d < minValue || d > maxValue {
-			t.Fatalf("Bad: %v", d)
+	tests := []struct {
+		Duration time.Duration
+		Buffer   time.Duration
+		Jitter   int64
+	}{
+		{
+			Duration: 1 * time.Minute,
+			Buffer:   10 * time.Second,
+			Jitter:   16,
+		},
+		{
+			Duration: 1 * time.Second,
+			Buffer:   500 * time.Millisecond,
+			Jitter:   4,
+		},
+		{
+			Duration: 1 * time.Second,
+			Buffer:   1 * time.Second,
+			Jitter:   4,
+		},
+		{
+			Duration: 1 * time.Second,
+			Buffer:   1 * time.Second,
+			Jitter:   0,
+		},
+		{
+			Duration: 1 * time.Second,
+			Buffer:   1 * time.Second,
+			Jitter:   1,
+		},
+	}
+
+	for _, test := range tests {
+		min, max := DurationMinusBufferDomain(test.Duration, test.Buffer, test.Jitter)
+		for i := 0; i < 10; i++ {
+			d := DurationMinusBuffer(test.Duration, test.Buffer, test.Jitter)
+			if d < min || d > max {
+				t.Fatalf("Bad: %v", d)
+			}
+		}
+	}
+}
+
+func TestDurationMinusBufferDomain(t *testing.T) {
+	tests := []struct {
+		Duration time.Duration
+		Buffer   time.Duration
+		Jitter   int64
+		Min      time.Duration
+		Max      time.Duration
+	}{
+		{
+			Duration: 60 * time.Second,
+			Buffer:   10 * time.Second,
+			Jitter:   16,
+			Min:      46*time.Second + 875*time.Millisecond,
+			Max:      50 * time.Second,
+		},
+		{
+			Duration: 60 * time.Second,
+			Buffer:   0 * time.Second,
+			Jitter:   16,
+			Min:      56*time.Second + 250*time.Millisecond,
+			Max:      60 * time.Second,
+		},
+		{
+			Duration: 60 * time.Second,
+			Buffer:   0 * time.Second,
+			Jitter:   0,
+			Min:      60 * time.Second,
+			Max:      60 * time.Second,
+		},
+		{
+			Duration: 60 * time.Second,
+			Buffer:   0 * time.Second,
+			Jitter:   1,
+			Min:      0 * time.Second,
+			Max:      60 * time.Second,
+		},
+		{
+			Duration: 60 * time.Second,
+			Buffer:   0 * time.Second,
+			Jitter:   2,
+			Min:      30 * time.Second,
+			Max:      60 * time.Second,
+		},
+		{
+			Duration: 60 * time.Second,
+			Buffer:   0 * time.Second,
+			Jitter:   4,
+			Min:      45 * time.Second,
+			Max:      60 * time.Second,
+		},
+		{
+			Duration: 0 * time.Second,
+			Buffer:   0 * time.Second,
+			Jitter:   0,
+			Min:      0 * time.Second,
+			Max:      0 * time.Second,
+		},
+		{
+			Duration: 60 * time.Second,
+			Buffer:   120 * time.Second,
+			Jitter:   8,
+			Min:      -1 * (52*time.Second + 500*time.Millisecond),
+			Max:      -1 * 60 * time.Second,
+		},
+	}
+
+	for _, test := range tests {
+		min, max := DurationMinusBufferDomain(test.Duration, test.Buffer, test.Jitter)
+		if min != test.Min {
+			t.Errorf("Bad min: %v != %v", min, test.Min)
+		}
+
+		if max != test.Max {
+			t.Errorf("Bad max: %v != %v", max, test.Max)
 		}
 	}
 }