diff --git a/google/internal/externalaccount/basecredentials.go b/google/internal/externalaccount/basecredentials.go
index ec0a1a9..13353d5 100644
--- a/google/internal/externalaccount/basecredentials.go
+++ b/google/internal/externalaccount/basecredentials.go
@@ -61,26 +61,30 @@ var (
 	validTokenURLPatterns = []*regexp.Regexp{
 		// The complicated part in the middle matches any number of characters that
 		// aren't period, spaces, or slashes.
-		regexp.MustCompile("^https://[^\\.\\s\\/\\\\]+\\.sts\\.googleapis\\.com$"),
-		regexp.MustCompile("^https://sts\\.googleapis\\.com$"),
-		regexp.MustCompile("^https://sts\\.[^\\.\\s\\/\\\\]+\\.googleapis\\.com$"),
-		regexp.MustCompile("^https://[^\\.\\s\\/\\\\]+-sts\\.googleapis\\.com$"),
+		regexp.MustCompile("^[^\\.\\s\\/\\\\]+\\.sts\\.googleapis\\.com$"),
+		regexp.MustCompile("^sts\\.googleapis\\.com$"),
+		regexp.MustCompile("^sts\\.[^\\.\\s\\/\\\\]+\\.googleapis\\.com$"),
+		regexp.MustCompile("^[^\\.\\s\\/\\\\]+-sts\\.googleapis\\.com$"),
 	}
 	validImpersonateURLPatterns = []*regexp.Regexp{
-		regexp.MustCompile("^https://[^\\.\\s\\/\\\\]+\\.iamcredentials\\.googleapis\\.com$"),
-		regexp.MustCompile("^https://iamcredentials\\.googleapis\\.com$"),
-		regexp.MustCompile("^https://iamcredentials\\.[^\\.\\s\\/\\\\]+\\.googleapis\\.com$"),
-		regexp.MustCompile("^https://[^\\.\\s\\/\\\\]+-iamcredentials\\.googleapis\\.com$"),
+		regexp.MustCompile("^[^\\.\\s\\/\\\\]+\\.iamcredentials\\.googleapis\\.com$"),
+		regexp.MustCompile("^iamcredentials\\.googleapis\\.com$"),
+		regexp.MustCompile("^iamcredentials\\.[^\\.\\s\\/\\\\]+\\.googleapis\\.com$"),
+		regexp.MustCompile("^[^\\.\\s\\/\\\\]+-iamcredentials\\.googleapis\\.com$"),
 	}
 )
 
-func validateURL(input string, patterns []*regexp.Regexp) bool {
+func validateURL(input string, patterns []*regexp.Regexp, scheme string) bool {
+	fmt.Println(input)
 	parsed, err := url.Parse(input)
 	if err != nil {
 		return false
 	}
-	path := parsed.Path
-	toTest := input[0 : len(input)-len(path)]
+	if parsed.Scheme != scheme {
+		return false
+	}
+	toTest := parsed.Host
+	fmt.Println(toTest)
 
 	for _, pattern := range patterns {
 		valid := pattern.MatchString(toTest)
@@ -93,22 +97,22 @@ func validateURL(input string, patterns []*regexp.Regexp) bool {
 
 // TokenSource Returns an external account TokenSource struct. This is to be called by package google to construct a google.Credentials.
 func (c *Config) TokenSource(ctx context.Context) (oauth2.TokenSource, error) {
-	return c.tokenSource(ctx, validTokenURLPatterns, validImpersonateURLPatterns)
+	return c.tokenSource(ctx, validTokenURLPatterns, validImpersonateURLPatterns, "https")
 }
 
 // tokenSource is a private function that's directly called by some of the tests,
 // because the unit test URLs are mocked, and would otherwise fail the
 // validity check.
-func (c *Config) tokenSource(ctx context.Context, tokenURLValidPats []*regexp.Regexp, impersonateURLValidPats []*regexp.Regexp) (oauth2.TokenSource, error) {
+func (c *Config) tokenSource(ctx context.Context, tokenURLValidPats []*regexp.Regexp, impersonateURLValidPats []*regexp.Regexp, scheme string) (oauth2.TokenSource, error) {
 	// Check the validity of TokenURL.
-	valid := validateURL(c.TokenURL, tokenURLValidPats)
+	valid := validateURL(c.TokenURL, tokenURLValidPats, scheme)
 	if !valid {
 		return nil, fmt.Errorf("oauth2/google: invalid TokenURL provided while constructing tokenSource")
 	}
 
 	// If ServiceAccountImpersonationURL is present, check its validity.
 	if c.ServiceAccountImpersonationURL != "" {
-		valid := validateURL(c.ServiceAccountImpersonationURL, impersonateURLValidPats)
+		valid := validateURL(c.ServiceAccountImpersonationURL, impersonateURLValidPats, scheme)
 		if !valid {
 			return nil, fmt.Errorf("oauth2/google: invalid ServiceAccountImpersonationURL provided while constructing tokenSource")
 		}
diff --git a/google/internal/externalaccount/basecredentials_test.go b/google/internal/externalaccount/basecredentials_test.go
index 2a23e5f..3189b16 100644
--- a/google/internal/externalaccount/basecredentials_test.go
+++ b/google/internal/externalaccount/basecredentials_test.go
@@ -118,7 +118,7 @@ func TestValidateURLTokenURL(t *testing.T) {
 	}
 	for _, tt := range urlValidityTests {
 		t.Run(" "+tt.input, func(t *testing.T) { // We prepend a space ahead of the test input when outputting for sake of readability.
-			valid := validateURL(tt.input, tt.pattern)
+			valid := validateURL(tt.input, tt.pattern, "https")
 			if valid != tt.result {
 				t.Errorf("got %v, want %v", valid, tt.result)
 			}
@@ -147,7 +147,7 @@ func TestValidateURLImpersonateURL(t *testing.T) {
 	}
 	for _, tt := range urlValidityTests {
 		t.Run(" "+tt.input, func(t *testing.T) { // We prepend a space ahead of the test input when outputting for sake of readability.
-			valid := validateURL(tt.input, tt.pattern)
+			valid := validateURL(tt.input, tt.pattern, "https")
 			if valid != tt.result {
 				t.Errorf("got %v, want %v", valid, tt.result)
 			}
diff --git a/google/internal/externalaccount/impersonate_test.go b/google/internal/externalaccount/impersonate_test.go
index 3d1fd23..d8eccf2 100644
--- a/google/internal/externalaccount/impersonate_test.go
+++ b/google/internal/externalaccount/impersonate_test.go
@@ -78,9 +78,8 @@ func TestImpersonation(t *testing.T) {
 	defer targetServer.Close()
 
 	testImpersonateConfig.TokenURL = targetServer.URL
-	allURLs := regexp.MustCompile(".*")
-	fmt.Println(allURLs)
-	ourTS, err := testImpersonateConfig.tokenSource(context.Background(), []*regexp.Regexp{allURLs}, []*regexp.Regexp{allURLs})
+	allURLs := regexp.MustCompile(".+")
+	ourTS, err := testImpersonateConfig.tokenSource(context.Background(), []*regexp.Regexp{allURLs}, []*regexp.Regexp{allURLs}, "http")
 	if err != nil {
 		fmt.Println(testImpersonateConfig.TokenURL)
 		t.Fatalf("Failed to create TokenSource: %v", err)