diff --git a/auth/authorization_code.go b/auth/authorization_code.go
index 142bac12f..a49c100e2 100644
--- a/auth/authorization_code.go
+++ b/auth/authorization_code.go
@@ -402,14 +402,23 @@ func (h *AuthorizationCodeHandler) Authorize(ctx context.Context, req *http.Requ
 }
 
 // resourceMetadataURLFromChallenges returns a resource metadata URL from the given "WWW-Authenticate" header challenges,
-// or the empty string if there is none.
+// preferring a "Bearer" challenge and otherwise the first other scheme that carries one. It returns the empty string if
+// there is none.
 func resourceMetadataURLFromChallenges(cs []oauthex.Challenge) string {
+	var fallback string
 	for _, c := range cs {
-		if u := c.Params["resource_metadata"]; u != "" {
+		u := c.Params["resource_metadata"]
+		if u == "" {
+			continue
+		}
+		if strings.EqualFold(c.Scheme, "Bearer") {
 			return u
 		}
+		if fallback == "" {
+			fallback = u
+		}
 	}
-	return ""
+	return fallback
 }
 
 // scopesFromChallenges returns the scopes from the given "WWW-Authenticate" header challenges.
diff --git a/auth/authorization_code_test.go b/auth/authorization_code_test.go
index 862514627..ee995e211 100644
--- a/auth/authorization_code_test.go
+++ b/auth/authorization_code_test.go
@@ -1606,3 +1606,24 @@ func TestInitialTokenSource(t *testing.T) {
 		t.Errorf("expected access token 'set_token', got '%s'", tok.AccessToken)
 	}
 }
+
+func TestResourceMetadataURLFromChallengesUsesBearerChallenge(t *testing.T) {
+	challenges := []oauthex.Challenge{
+		{Scheme: "Basic", Params: map[string]string{"resource_metadata": "https://basic.example/metadata"}},
+		{Scheme: "Bearer", Params: map[string]string{"resource_metadata": "https://bearer.example/metadata"}},
+	}
+	if got, want := resourceMetadataURLFromChallenges(challenges), "https://bearer.example/metadata"; got != want {
+		t.Errorf("resourceMetadataURLFromChallenges() = %q, want %q", got, want)
+	}
+}
+
+func TestResourceMetadataURLFromChallengesFallsBackToOtherSchemes(t *testing.T) {
+	challenges := []oauthex.Challenge{
+		{Scheme: "Basic", Params: map[string]string{}},
+		{Scheme: "Digest", Params: map[string]string{"resource_metadata": "https://digest.example/metadata"}},
+		{Scheme: "Basic", Params: map[string]string{"resource_metadata": "https://basic.example/metadata"}},
+	}
+	if got, want := resourceMetadataURLFromChallenges(challenges), "https://digest.example/metadata"; got != want {
+		t.Errorf("resourceMetadataURLFromChallenges() = %q, want %q", got, want)
+	}
+}
diff --git a/auth/extauth/client_credentials.go b/auth/extauth/client_credentials.go
index c65d8b066..cdd99b8fb 100644
--- a/auth/extauth/client_credentials.go
+++ b/auth/extauth/client_credentials.go
@@ -236,14 +236,24 @@ func protectedResourceMetadataURLs(metadataURL, resourceURL string) []prmURL {
 }
 
 // resourceMetadataURLFromChallenges returns a resource metadata URL from
-// WWW-Authenticate challenges, or the empty string if there is none.
+// WWW-Authenticate challenges, preferring a Bearer challenge and otherwise the
+// first other scheme that carries one. It returns the empty string if there is
+// none.
 func resourceMetadataURLFromChallenges(cs []oauthex.Challenge) string {
+	var fallback string
 	for _, c := range cs {
-		if u := c.Params["resource_metadata"]; u != "" {
+		u := c.Params["resource_metadata"]
+		if u == "" {
+			continue
+		}
+		if strings.EqualFold(c.Scheme, "Bearer") {
 			return u
 		}
+		if fallback == "" {
+			fallback = u
+		}
 	}
-	return ""
+	return fallback
 }
 
 // scopesFromChallenges returns scopes from WWW-Authenticate challenges.
diff --git a/auth/extauth/client_credentials_test.go b/auth/extauth/client_credentials_test.go
index b2973de7c..8c87bb537 100644
--- a/auth/extauth/client_credentials_test.go
+++ b/auth/extauth/client_credentials_test.go
@@ -418,3 +418,24 @@ func TestSelectTokenAuthMethod(t *testing.T) {
 		})
 	}
 }
+
+func TestResourceMetadataURLFromChallengesUsesBearerChallenge(t *testing.T) {
+	challenges := []oauthex.Challenge{
+		{Scheme: "Basic", Params: map[string]string{"resource_metadata": "https://basic.example/metadata"}},
+		{Scheme: "Bearer", Params: map[string]string{"resource_metadata": "https://bearer.example/metadata"}},
+	}
+	if got, want := resourceMetadataURLFromChallenges(challenges), "https://bearer.example/metadata"; got != want {
+		t.Errorf("resourceMetadataURLFromChallenges() = %q, want %q", got, want)
+	}
+}
+
+func TestResourceMetadataURLFromChallengesFallsBackToOtherSchemes(t *testing.T) {
+	challenges := []oauthex.Challenge{
+		{Scheme: "Basic", Params: map[string]string{}},
+		{Scheme: "Digest", Params: map[string]string{"resource_metadata": "https://digest.example/metadata"}},
+		{Scheme: "Basic", Params: map[string]string{"resource_metadata": "https://basic.example/metadata"}},
+	}
+	if got, want := resourceMetadataURLFromChallenges(challenges), "https://digest.example/metadata"; got != want {
+		t.Errorf("resourceMetadataURLFromChallenges() = %q, want %q", got, want)
+	}
+}