diff --git a/loader/cdnjs.go b/loader/cdnjs.go
index b9a785dea16..f58719c7a50 100644
--- a/loader/cdnjs.go
+++ b/loader/cdnjs.go
@@ -17,7 +17,7 @@ type cdnjsEnvelope struct {
 	}
 }
 
-func cdnjs(logger logrus.FieldLogger, specifier string, parts []string) (string, error) {
+func cdnjs(logger logrus.FieldLogger, path string, parts []string) (string, error) {
 	name := parts[0]
 	version := parts[1]
 	filename := parts[2]
@@ -56,7 +56,7 @@ func cdnjs(logger logrus.FieldLogger, specifier string, parts []string) (string,
 			if len(ver.Files) == 0 {
 				return "",
 					fmt.Errorf("cdnjs: no files for version %s of %s, this is a problem with the library or cdnjs not k6",
-						version, specifier)
+						version, path)
 			}
 			backupFilename = ver.Files[0]
 			for _, file := range ver.Files {
@@ -70,7 +70,5 @@ func cdnjs(logger logrus.FieldLogger, specifier string, parts []string) (string,
 		}
 	}
 
-	realURL := "https://cdnjs.cloudflare.com/ajax/libs/" + name + "/" + version + "/" + filename
-	logger.Warnf(magicURLsDeprecationWarning, specifier, "cdnjs", realURL)
-	return realURL, nil
+	return "https://cdnjs.cloudflare.com/ajax/libs/" + name + "/" + version + "/" + filename, nil
 }
diff --git a/loader/github.go b/loader/github.go
index 897d10de3d3..028d8c773b6 100644
--- a/loader/github.go
+++ b/loader/github.go
@@ -2,14 +2,9 @@ package loader
 
 import "github.com/sirupsen/logrus"
 
-func github(logger logrus.FieldLogger, specifier string, parts []string) (string, error) {
+func github(_ logrus.FieldLogger, _ string, parts []string) (string, error) {
 	username := parts[0]
 	repo := parts[1]
 	filepath := parts[2]
-	realURL := "https://raw.githubusercontent.com/" + username + "/" + repo + "/master/" + filepath
-	logger.Warnf(magicURLsDeprecationWarning, specifier, "github", realURL)
-	return realURL, nil
+	return "https://raw.githubusercontent.com/" + username + "/" + repo + "/master/" + filepath, nil
 }
-
-const magicURLsDeprecationWarning = "Specifier %q resolved to use a non-conventional %s loader. " +
-	"That loader is deprecated and will be removed in v0.53.0. Please use the real URL %q instead."
diff --git a/loader/loader.go b/loader/loader.go
index 5f8a1403033..24413512939 100644
--- a/loader/loader.go
+++ b/loader/loader.go
@@ -170,6 +170,10 @@ func Load(
 	data, err := fsext.ReadFile(filesystems[scheme], pathOnFs)
 
 	if err == nil {
+		if moduleSpecifier.Opaque != "" {
+			loaderName, _, _ := pickLoader(moduleSpecifier.Opaque)
+			logger.Warnf(magicURLsDeprecationWarning, originalModuleSpecifier, loaderName)
+		}
 		return &SourceData{URL: moduleSpecifier, Data: data}, nil
 	}
 	if !errors.Is(err, fs.ErrNotExist) {
@@ -203,13 +207,20 @@ func Load(
 	return result, nil
 }
 
+const (
+	magicURLsDeprecationWarning = "Specifier %q resolved to use a non-conventional %[2]q loader. " +
+		"The used %[2]q loader is deprecated and will be removed in k6 v0.53.0."
+	magicURLsDeprecationWarningExtended = magicURLsDeprecationWarning + " Please use the real URL %q instead."
+)
+
 func resolveUsingLoaders(logger logrus.FieldLogger, name string) (*url.URL, error) {
-	_, loader, loaderArgs := pickLoader(name)
+	loaderName, loader, loaderArgs := pickLoader(name)
 	if loader != nil {
 		urlString, err := loader(logger, name, loaderArgs)
 		if err != nil {
 			return nil, err
 		}
+		logger.Warnf(magicURLsDeprecationWarningExtended, name, loaderName, urlString)
 		return url.Parse(urlString)
 	}