diff --git a/dht/closest_nodes.go b/dht/closest_nodes.go
index a677a2e6..70366dd5 100644
--- a/dht/closest_nodes.go
+++ b/dht/closest_nodes.go
@@ -12,7 +12,7 @@ type nodeMaxHeap struct {
 func (me nodeMaxHeap) Len() int { return len(me.IDs) }
 
 func (me nodeMaxHeap) Less(i, j int) bool {
-	return idDistance(me.IDs[i], me.Target) > idDistance(me.IDs[j], me.Target)
+	return idDistance(me.IDs[i], me.Target).Cmp(idDistance(me.IDs[j], me.Target)) > 0
 }
 
 func (me *nodeMaxHeap) Pop() (ret interface{}) {
diff --git a/dht/dht.go b/dht/dht.go
index 6e5d29cb..094a6bc6 100644
--- a/dht/dht.go
+++ b/dht/dht.go
@@ -8,6 +8,7 @@ import (
 	"fmt"
 	"io"
 	"log"
+	"math/big"
 	"net"
 	"os"
 	"sync"
@@ -901,19 +902,116 @@ func (s *Server) Close() {
 	s.mu.Unlock()
 }
 
-func idDistance(a, b string) (ret int) {
-	if len(a) != 20 {
-		panic(a)
+type distance interface {
+	Cmp(distance) int
+	BitCount() int
+	IsZero() bool
+}
+
+type bigIntDistance struct {
+	*big.Int
+}
+
+// How many bits?
+func bitCount(n *big.Int) int {
+	var count int = 0
+	for _, b := range n.Bytes() {
+		count += int(bitCounts[b])
 	}
-	if len(b) != 20 {
-		panic(b)
+	return count
+}
+
+// The bit counts for each byte value (0 - 255).
+var bitCounts = []int8{
+	// Generated by Java BitCount of all values from 0 to 255
+	0, 1, 1, 2, 1, 2, 2, 3,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	5, 6, 6, 7, 6, 7, 7, 8,
+}
+
+func (me bigIntDistance) BitCount() int {
+	return bitCount(me.Int)
+}
+
+func (me bigIntDistance) Cmp(d distance) int {
+	return me.Int.Cmp(d.(bigIntDistance).Int)
+}
+
+func (me bigIntDistance) IsZero() bool {
+	return me.Int.Cmp(big.NewInt(0)) == 0
+}
+
+type bitCountDistance int
+
+func (me bitCountDistance) BitCount() int { return int(me) }
+
+func (me bitCountDistance) Cmp(rhs distance) int {
+	rhs_ := rhs.(bitCountDistance)
+	if me < rhs_ {
+		return -1
+	} else if me == rhs_ {
+		return 0
+	} else {
+		return 1
 	}
-	for i := 0; i < 20; i++ {
-		for j := uint(0); j < 8; j++ {
-			ret += int(a[i]>>j&1 ^ b[i]>>j&1)
+}
+
+func (me bitCountDistance) IsZero() bool {
+	return me == 0
+}
+
+func idDistance(a, b string) distance {
+	if true {
+		if len(a) != 20 {
+			panic(a)
 		}
+		if len(b) != 20 {
+			panic(b)
+		}
+		x := new(big.Int)
+		y := new(big.Int)
+		x.SetBytes([]byte(a))
+		y.SetBytes([]byte(b))
+		dist := new(big.Int)
+		return bigIntDistance{dist.Xor(x, y)}
+	} else {
+		ret := 0
+		for i := 0; i < 20; i++ {
+			for j := uint(0); j < 8; j++ {
+				ret += int(a[i]>>j&1 ^ b[i]>>j&1)
+			}
+		}
+		return bitCountDistance(ret)
 	}
-	return
 }
 
 func (s *Server) closestGoodNodes(k int, targetID string) []*Node {
diff --git a/dht/dht_test.go b/dht/dht_test.go
index 71afc5eb..5b5b5d1d 100644
--- a/dht/dht_test.go
+++ b/dht/dht_test.go
@@ -1,11 +1,17 @@
 package dht
 
 import (
+	"math/big"
 	"math/rand"
 	"net"
 	"testing"
 )
 
+func TestSetNilBigInt(t *testing.T) {
+	i := new(big.Int)
+	i.SetBytes(make([]byte, 2))
+}
+
 func TestMarshalCompactNodeInfo(t *testing.T) {
 	cni := NodeInfo{
 		ID: [20]byte{'a', 'b', 'c'},
@@ -49,13 +55,13 @@ var testIDs = []string{
 }
 
 func TestDistances(t *testing.T) {
-	if idDistance(testIDs[3], testIDs[0]) != 4+8+4+4 {
+	if idDistance(testIDs[3], testIDs[0]).BitCount() != 4+8+4+4 {
 		t.FailNow()
 	}
-	if idDistance(testIDs[3], testIDs[1]) != 4+8+4+4 {
+	if idDistance(testIDs[3], testIDs[1]).BitCount() != 4+8+4+4 {
 		t.FailNow()
 	}
-	if idDistance(testIDs[3], testIDs[2]) != 4+8+8 {
+	if idDistance(testIDs[3], testIDs[2]).BitCount() != 4+8+8 {
 		t.FailNow()
 	}
 }
@@ -71,17 +77,17 @@ func TestBadIdStrings(t *testing.T) {
 	recoverPanicOrDie(t, func() {
 		idDistance(zeroID, b)
 	})
-	if idDistance(zeroID, zeroID) != 0 {
-		t.FailNow()
+	if !idDistance(zeroID, zeroID).IsZero() {
+		t.Fatal("identical IDs should have distance 0")
 	}
 	a = "\x03" + zeroID[1:]
 	b = zeroID
-	if idDistance(a, b) != 2 {
+	if idDistance(a, b).BitCount() != 2 {
 		t.FailNow()
 	}
 	a = "\x03" + zeroID[1:18] + "\x55\xf0"
 	b = "\x55" + zeroID[1:17] + "\xff\x55\x0f"
-	if c := idDistance(a, b); c != 20 {
+	if c := idDistance(a, b).BitCount(); c != 20 {
 		t.Fatal(c)
 	}
 }