diff --git a/cuckoofilter.go b/cuckoofilter.go
index fef219f..c464d87 100644
--- a/cuckoofilter.go
+++ b/cuckoofilter.go
@@ -4,7 +4,9 @@ import (
 	"bytes"
 	"encoding/binary"
 	"fmt"
-	"math/rand"
+	"time"
+
+	"github.com/dgryski/go-wyhash"
 )
 
 // maxCuckooKickouts is the maximum number of times reinsert
@@ -18,6 +20,9 @@ type Filter struct {
 	// Bit mask set to len(buckets) - 1. As len(buckets) is always a power of 2,
 	// applying this mask mimics the operation x % len(buckets).
 	bucketIndexMask uint
+	// rng is a simple pseudo-random number generator that we store locally
+	// so that we don't have to spend time locking the global RNG.
+	rng *wyhash.Rng
 }
 
 // NewFilter returns a new cuckoofilter suitable for the given number of elements.
@@ -33,10 +38,12 @@ func NewFilter(numElements uint) *Filter {
 		numBuckets = 1
 	}
 	buckets := make([]bucket, numBuckets)
+	rng := wyhash.Rng(time.Now().UnixNano())
 	return &Filter{
 		buckets:         buckets,
 		count:           0,
 		bucketIndexMask: uint(len(buckets) - 1),
+		rng:             &rng,
 	}
 }
 
@@ -72,7 +79,26 @@ func (cf *Filter) Insert(data []byte) bool {
 	if cf.insert(fp, i2) {
 		return true
 	}
-	return cf.reinsert(fp, randi(i1, i2))
+	return cf.reinsert(fp, cf.Coinflip(i1, i2))
+}
+
+// Using % isn't *perfectly* uniform, but it really only matters when n is a
+// significant fraction of the rng's range. It's more than good enough for our
+// purposes since n is on the order of 10^6 and our rng is 63 bits (10^19); this
+// means the bias is on the order of 10^-13. For our use case, that's well below
+// the noise floor.
+func (cf *Filter) Intn(n int) int {
+	// we need to make sure it's strictly positive, so mask off the sign bit
+	return int(cf.rng.Next()&0x7FFF_FFFF_FFFF_FFFF) % n
+}
+
+// Coinflip returns either i1 or i2 randomly by examining the least significant
+// bit of the RNG.
+func (cf Filter) Coinflip(i1, i2 uint) uint {
+	if cf.rng.Next()&0x1 == 0 {
+		return i1
+	}
+	return i2
 }
 
 func (cf *Filter) insert(fp fingerprint, i uint) bool {
@@ -85,7 +111,7 @@ func (cf *Filter) insert(fp fingerprint, i uint) bool {
 
 func (cf *Filter) reinsert(fp fingerprint, i uint) bool {
 	for k := 0; k < maxCuckooKickouts; k++ {
-		j := rand.Intn(bucketSize)
+		j := cf.Intn(bucketSize)
 		// Swap fingerprint with bucket entry.
 		cf.buckets[i][j], fp = fp, cf.buckets[i][j]
 
diff --git a/cuckoofilter_test.go b/cuckoofilter_test.go
index 08d4ca1..c43b91c 100644
--- a/cuckoofilter_test.go
+++ b/cuckoofilter_test.go
@@ -3,7 +3,6 @@ package cuckoo
 import (
 	"bufio"
 	"fmt"
-	"math"
 	"math/rand"
 	"os"
 	"testing"
@@ -11,13 +10,6 @@ import (
 	"github.com/google/go-cmp/cmp"
 )
 
-// optFloatNear considers float64 as equal if the relative delta is small.
-var optFloatNear = cmp.Comparer(func(x, y float64) bool {
-	delta := math.Abs(x - y)
-	mean := math.Abs(x+y) / 2.0
-	return delta/mean < 0.00001
-})
-
 func TestInsertion(t *testing.T) {
 	cf := NewFilter(1000000)
 	fd, err := os.Open("/usr/share/dict/words")
@@ -257,3 +249,44 @@ func TestEncodeDecode(t *testing.T) {
 		t.Errorf("Decode = %v, want %v, encoded = %v", got, cf, encoded)
 	}
 }
+
+func TestFilter_Coinflip(t *testing.T) {
+	cf := NewFilter(8)
+	yes := 0
+	for i := 0; i < 1000000; i++ {
+		if cf.Coinflip(0, 1) == 1 {
+			yes++
+		}
+	}
+	// See below -- we're checking that we're within 1% of the expected value.
+	if yes < 499000 || yes > 501000 {
+		t.Errorf("yes: %d, expected 500000", yes)
+	}
+}
+
+func TestFilter_Intn(t *testing.T) {
+	const tries = 1_000_000
+	for _, n := range []int{10, 100, 1000} {
+		t.Run(fmt.Sprintf("n=%d", n), func(t *testing.T) {
+			cf := NewFilter(8)
+			yes := 0
+			buckets := make([]int, n)
+			for i := 0; i < tries; i++ {
+				x := cf.Intn(n)
+				buckets[x]++
+				if x == 0 {
+					yes++
+				}
+			}
+			// this is a rectangular distribution, so the expected value is
+			// tries / n. We expect the actual value to be within 10% of that.
+			// This means that the test will randomly fail occasionally, but it
+			// should be rare.
+			expected := tries / n
+			if yes < (expected*90)/100 || yes > (expected*110)/100 {
+				t.Errorf("yes: %d, expected between %d and %d", yes, (expected*95)/100, (expected*105)/100)
+				t.Log(buckets)
+			}
+		})
+	}
+}
diff --git a/go.mod b/go.mod
index f261456..95ed942 100644
--- a/go.mod
+++ b/go.mod
@@ -4,5 +4,6 @@ go 1.15
 
 require (
 	github.com/dgryski/go-metro v0.0.0-20200812162917-85c65e2d0165
+	github.com/dgryski/go-wyhash v0.0.0-20191203203029-c4841ae36371
 	github.com/google/go-cmp v0.5.9
 )
diff --git a/go.sum b/go.sum
index aabbb23..ab99de0 100644
--- a/go.sum
+++ b/go.sum
@@ -1,4 +1,6 @@
 github.com/dgryski/go-metro v0.0.0-20200812162917-85c65e2d0165 h1:BS21ZUJ/B5X2UVUbczfmdWH7GapPWAhxcMsDnjJTU1E=
 github.com/dgryski/go-metro v0.0.0-20200812162917-85c65e2d0165/go.mod h1:c9O8+fpSOX1DM8cPNSkX/qsBWdkD4yd2dpciOWQjpBw=
+github.com/dgryski/go-wyhash v0.0.0-20191203203029-c4841ae36371 h1:bz5ApY1kzFBvw3yckuyRBCtqGvprWrKswYK468nm+Gs=
+github.com/dgryski/go-wyhash v0.0.0-20191203203029-c4841ae36371/go.mod h1:/ENMIO1SQeJ5YQeUWWpbX8f+bS8INHrrhFjXgEqi4LA=
 github.com/google/go-cmp v0.5.9 h1:O2Tfq5qg4qc4AmwVlvv0oLiVAGB7enBSJ2x2DqQFi38=
 github.com/google/go-cmp v0.5.9/go.mod h1:17dUlkBOakJ0+DkrSSNjCkIjxS6bF9zb3elmeNGIjoY=
diff --git a/util.go b/util.go
index 00f6309..e84c414 100644
--- a/util.go
+++ b/util.go
@@ -2,19 +2,11 @@ package cuckoo
 
 import (
 	"encoding/binary"
-	"math/rand"
+	"math/bits"
 
 	metro "github.com/dgryski/go-metro"
 )
 
-// randi returns either i1 or i2 randomly.
-func randi(i1, i2 uint) uint {
-	if rand.Int31()%2 == 0 {
-		return i1
-	}
-	return i2
-}
-
 func getAltIndex(fp fingerprint, i uint, bucketIndexMask uint) uint {
 	b := make([]byte, 2)
 	binary.LittleEndian.PutUint16(b, uint16(fp))
@@ -40,13 +32,5 @@ func getIndexAndFingerprint(data []byte, bucketIndexMask uint) (uint, fingerprin
 }
 
 func getNextPow2(n uint64) uint {
-	n--
-	n |= n >> 1
-	n |= n >> 2
-	n |= n >> 4
-	n |= n >> 8
-	n |= n >> 16
-	n |= n >> 32
-	n++
-	return uint(n)
+	return uint(1 << bits.Len64(n-1))
 }