diff --git a/wgengine/magicsock/magicsock.go b/wgengine/magicsock/magicsock.go
index 123b2e70b..95af25891 100644
--- a/wgengine/magicsock/magicsock.go
+++ b/wgengine/magicsock/magicsock.go
@@ -4921,6 +4921,28 @@ func betterAddr(a, b addrLatency) bool {
 			return false
 		}
 	}
+
+	// If we get here, then both addresses are the same IP type (i.e. both
+	// IPv4 or both IPv6). All decisions below are made solely on latency.
+	//
+	// Determine how much the latencies differ; we ensure the larger
+	// latency is the denominator, so this fraction will always be <= 1.0.
+	var latencyFraction float64
+	if a.latency >= b.latency {
+		latencyFraction = float64(b.latency) / float64(a.latency)
+	} else {
+		latencyFraction = float64(a.latency) / float64(b.latency)
+	}
+
+	// Don't change anything if the latency improvement is less than 1%; we
+	// want a bit of "stickiness" (a.k.a. hysteresis) to avoid flapping if
+	// there's two roughly-equivalent endpoints.
+	if latencyFraction >= 0.99 {
+		return false
+	}
+
+	// The total difference is >1%, so a is better than b if it's
+	// lower-latency.
 	return a.latency < b.latency
 }
 
diff --git a/wgengine/magicsock/magicsock_test.go b/wgengine/magicsock/magicsock_test.go
index c050cfc20..9115a3eea 100644
--- a/wgengine/magicsock/magicsock_test.go
+++ b/wgengine/magicsock/magicsock_test.go
@@ -1633,9 +1633,13 @@ func TestBetterAddr(t *testing.T) {
 		{a: zero, b: zero, want: false},
 		{a: al("10.0.0.2:123", 5*ms), b: zero, want: true},
 		{a: zero, b: al("10.0.0.2:123", 5*ms), want: false},
-		{a: al("10.0.0.2:123", 5*ms), b: al("1.2.3.4:555", 6*ms), want: true},
+		{a: al("10.0.0.2:123", 5*ms), b: al("1.2.3.4:555", 10*ms), want: true},
 		{a: al("10.0.0.2:123", 5*ms), b: al("10.0.0.2:123", 10*ms), want: false}, // same IPPort
 
+		// Don't prefer b to a if it's not substantially better.
+		{a: al("10.0.0.2:123", 100*ms), b: al("1.2.3.4:555", 101*ms), want: false},
+		{a: al("10.0.0.2:123", 100*ms), b: al("1.2.3.4:555", 103*ms), want: true},
+
 		// Prefer IPv6 if roughly equivalent:
 		{
 			a:    al("[2001::5]:123", 100*ms),