diff --git a/autopilot/prefattach_test.go b/autopilot/prefattach_test.go
index 5801c00d..f485ce7d 100644
--- a/autopilot/prefattach_test.go
+++ b/autopilot/prefattach_test.go
@@ -376,6 +376,12 @@ func TestConstrainedPrefAttachmentSelectTwoVertexes(t *testing.T) {
 				t1.Fatalf("unable to generate channel: %v", err)
 			}
 
+			// We also add a third, non-connected node to the graph.
+			_, err = graph.addRandNode()
+			if err != nil {
+				t1.Fatalf("unable to add random node: %v", err)
+			}
+
 			// Get the score for all nodes found in the graph at
 			// this point.
 			nodes := make(map[NodeID]struct{})
@@ -386,7 +392,7 @@ func TestConstrainedPrefAttachmentSelectTwoVertexes(t *testing.T) {
 				t1.Fatalf("unable to traverse graph: %v", err)
 			}
 
-			if len(nodes) != 2 {
+			if len(nodes) != 3 {
 				t1.Fatalf("expected 2 nodes, found %d", len(nodes))
 			}
 
@@ -401,8 +407,10 @@ func TestConstrainedPrefAttachmentSelectTwoVertexes(t *testing.T) {
 					"directives: %v", err)
 			}
 
-			if len(candidates) != len(nodes) {
-				t1.Fatalf("all nodes should be scored, "+
+			// We expect two candidates, since one of the nodes
+			// doesn't have any channels.
+			if len(candidates) != 2 {
+				t1.Fatalf("2 nodes should be scored, "+
 					"instead %v were", len(candidates))
 			}