dht/dht.go      | 25 +++++++++++++++++++++++++
 dht/dht_test.go | 28 +++++++++++++++++++++++-----

diff --git a/dht/dht.go b/dht/dht.go
index d688f770b9af79d25bd4ad91204fd20ba1a1c149..d1abce948e239d182a44933d1e674e86889f64bc 100644
--- a/dht/dht.go
+++ b/dht/dht.go
@@ -1104,8 +1104,33 @@ 	return me == 0
 }
 
 // Below are 2 versions of idDistance. Only one can be active.
+var maxDistance big.Int
 
+func init() {
+	var zero big.Int
+	maxDistance.SetBit(&zero, 160, 1)
+}
+
+// If we don't know the ID for a node, then its distance is more than the
+// furthest possible distance otherwise.
 func idDistance(a, b string) (ret bigIntDistance) {
+	if a == "" && b == "" {
+		return
+	}
+	if a == "" {
+		if len(b) != 20 {
+			panic(b)
+		}
+		ret.Set(&maxDistance)
+		return
+	}
+	if b == "" {
+		if len(a) != 20 {
+			panic(a)
+		}
+		ret.Set(&maxDistance)
+		return
+	}
 	if len(a) != 20 {
 		panic(a)
 	}
diff --git a/dht/dht_test.go b/dht/dht_test.go
index 5b5b5d1d5fdbe055a9069c97feafc9ec5b6c60ba..137aa1366ee2f6e37ef0a4bba7afd119be323f86 100644
--- a/dht/dht_test.go
+++ b/dht/dht_test.go
@@ -52,6 +52,7 @@ 	"\x03" + zeroID[1:],
 	"\x03" + zeroID[1:18] + "\x55\xf0",
 	"\x55" + zeroID[1:17] + "\xff\x55\x0f",
 	"\x54" + zeroID[1:18] + "\x50\x0f",
+	"",
 }
 
 func TestDistances(t *testing.T) {
@@ -63,22 +64,39 @@ 		t.FailNow()
 	}
 	if idDistance(testIDs[3], testIDs[2]).BitCount() != 4+8+8 {
 		t.FailNow()
+	}
+	for i := 0; i < 5; i++ {
+		dist := idDistance(testIDs[i], testIDs[5]).Int
+		if dist.Cmp(&maxDistance) != 0 {
+			t.FailNow()
+		}
+	}
+}
+
+func TestMaxDistanceString(t *testing.T) {
+	if string(maxDistance.Bytes()) != "\x01"+zeroID {
+		t.FailNow()
 	}
 }
 
 func TestBadIdStrings(t *testing.T) {
 	var a, b string
+	idDistance(a, b)
+	idDistance(a, zeroID)
+	idDistance(zeroID, b)
 	recoverPanicOrDie(t, func() {
-		idDistance(a, b)
+		idDistance("when", a)
 	})
 	recoverPanicOrDie(t, func() {
-		idDistance(a, zeroID)
+		idDistance(a, "bad")
 	})
 	recoverPanicOrDie(t, func() {
-		idDistance(zeroID, b)
+		idDistance("meets", "evil")
 	})
-	if !idDistance(zeroID, zeroID).IsZero() {
-		t.Fatal("identical IDs should have distance 0")
+	for _, id := range testIDs {
+		if !idDistance(id, id).IsZero() {
+			t.Fatal("identical IDs should have distance 0")
+		}
 	}
 	a = "\x03" + zeroID[1:]
 	b = zeroID