diff --git a/ssh/client_auth.go b/ssh/client_auth.go
index 5b7aa30..c41e163 100644
--- a/ssh/client_auth.go
+++ b/ssh/client_auth.go
@@ -41,15 +41,17 @@ func (c *connection) clientAuthenticate(config *ClientConfig) error {
 		tried[auth.method()] = true
 
 		auth = nil
+
+	findNext:
 		for _, a := range config.Auth {
 			candidateMethod := a.method()
+			if tried[candidateMethod] {
+				continue
+			}
 			for _, meth := range methods {
-				if meth != candidateMethod {
-					continue
-				}
-				if !tried[meth] {
+				if meth == candidateMethod {
 					auth = a
-					break
+					break findNext
 				}
 			}
 		}
diff --git a/ssh/client_auth_test.go b/ssh/client_auth_test.go
index 3173255..e6b979f 100644
--- a/ssh/client_auth_test.go
+++ b/ssh/client_auth_test.go
@@ -111,6 +111,29 @@ func TestAuthMethodPassword(t *testing.T) {
 	}
 }
 
+func TestAuthMethodFallback(t *testing.T) {
+	var passwordCalled bool
+	config := &ClientConfig{
+		User: "testuser",
+		Auth: []AuthMethod{
+			PublicKeys(testSigners["rsa"]),
+			PasswordCallback(
+				func() (string, error) {
+					passwordCalled = true
+					return "WRONG", nil
+				}),
+		},
+	}
+
+	if err := tryAuth(t, config); err != nil {
+		t.Fatalf("unable to dial remote side: %s", err)
+	}
+
+	if passwordCalled {
+		t.Errorf("password auth tried before public-key auth.")
+	}
+}
+
 func TestAuthMethodWrongPassword(t *testing.T) {
 	config := &ClientConfig{
 		User: "testuser",