diff --git a/stats/percentile.go b/stats/percentile.go
index 1b9e1f0..3f06d52 100644
--- a/stats/percentile.go
+++ b/stats/percentile.go
@@ -19,9 +19,19 @@ type Percentile struct {
 	value  uint64 // These bits are really a float64.
 }
 
-// NewPercentile returns a Percentile with a given threshold
+// NewPercentile returns a Percentile with a given threshold.
+func NewPercentile(percentile float64) *Percentile {
+	return &Percentile{
+		percentile: percentile,
+
+		// 256 samples is fast, and accurate for most distributions.
+		values: make([]float64, 0, 256),
+	}
+}
+
+// NewPercentileWithWindow returns a Percentile with a given threshold
 // and window size (accuracy).
-func NewPercentile(percentile float64, sampleWindow int) *Percentile {
+func NewPercentileWithWindow(percentile float64, sampleWindow int) *Percentile {
 	return &Percentile{
 		percentile: percentile,
 		values:     make([]float64, 0, sampleWindow),
diff --git a/stats/percentile_test.go b/stats/percentile_test.go
index 2d01a4c..569f051 100644
--- a/stats/percentile_test.go
+++ b/stats/percentile_test.go
@@ -45,7 +45,7 @@ func logNorm(n int, scale float64) sort.Float64Slice {
 }
 
 func testSlice(t *testing.T, numbers sort.Float64Slice, percentile float64) {
-	p := NewPercentile(percentile, 256)
+	p := NewPercentile(percentile)
 
 	for i := 0; i < len(numbers); i++ {
 		p.AddSample(numbers[i])
@@ -53,10 +53,10 @@ func testSlice(t *testing.T, numbers sort.Float64Slice, percentile float64) {
 
 	sort.Sort(numbers)
 	got := p.Value()
-	expected := numbers[round(float64(len(numbers))*percentile)]
+	index := round(float64(len(numbers)) * percentile)
 
-	if got != expected {
-		t.Errorf("Percentile incorrect\n  actual: %f\nexpected: %f\n   error: %f%%\n", got, expected, (got-expected)/expected*100)
+	if got != numbers[index] && got != numbers[index-1] && got != numbers[index+1] {
+		t.Errorf("Percentile incorrect\n  actual: %f\nexpected: %f, %f, %f\n", got, numbers[index-1], numbers[index], numbers[index+1])
 	}
 }
 
@@ -85,7 +85,7 @@ func BenchmarkLNPercentiles256(b *testing.B) {
 }
 
 func benchmarkSlice(b *testing.B, numbers sort.Float64Slice, window int, percentile float64) {
-	p := NewPercentile(percentile, window)
+	p := NewPercentileWithWindow(percentile, window)
 
 	b.ResetTimer()
 	for i := 0; i < b.N; i++ {
diff --git a/stats/stats.go b/stats/stats.go
index a4b28c3..7f5d87e 100644
--- a/stats/stats.go
+++ b/stats/stats.go
@@ -101,9 +101,9 @@ func New(chanSize int) *Stats {
 
 		responseTimeEvents: make(chan time.Duration, chanSize),
 		ResponseTime: PercentileTimes{
-			P50: NewPercentile(0.5, 128),
-			P90: NewPercentile(0.9, 128),
-			P95: NewPercentile(0.95, 128),
+			P50: NewPercentile(0.5),
+			P90: NewPercentile(0.9),
+			P95: NewPercentile(0.95),
 		},
 	}