diff --git a/jvm/src/test/scala/scala/xml/parsing/ConstructingParserTest.scala b/jvm/src/test/scala/scala/xml/parsing/ConstructingParserTest.scala
index 413cd9a74..fb8590d00 100644
--- a/jvm/src/test/scala/scala/xml/parsing/ConstructingParserTest.scala
+++ b/jvm/src/test/scala/scala/xml/parsing/ConstructingParserTest.scala
@@ -75,10 +75,22 @@ class ConstructingParserTest {
   @Test
   def SI6341issue65: Unit = {
     val str = """<elem one="test" two="test2" three="test3"/>"""
-    val cpa = ConstructingParser.fromSource(io.Source.fromString(str), preserveWS = true)
+    val cpa = ConstructingParser.fromSource(Source.fromString(str), preserveWS = true)
     val cpadoc = cpa.document()
     val ppr = new PrettyPrinter(80,5)
     val out = ppr.format(cpadoc.docElem)
     assertEquals(str, out)
   }
+
+  // https://github.com/scala/scala-xml/issues/541
+  @Test
+  def issue541: Unit = {
+    val xml =
+      """|<script>// <![CDATA[
+         |[]; // ]]>
+         |</script>""".stripMargin
+    val parser = ConstructingParser.fromSource(Source.fromString(xml), preserveWS = true)
+    parser.document().docElem  // shouldn't crash
+  }
+
 }
diff --git a/shared/src/main/scala/scala/xml/parsing/MarkupParser.scala b/shared/src/main/scala/scala/xml/parsing/MarkupParser.scala
index 95ec2ec55..acd19485e 100755
--- a/shared/src/main/scala/scala/xml/parsing/MarkupParser.scala
+++ b/shared/src/main/scala/scala/xml/parsing/MarkupParser.scala
@@ -58,7 +58,10 @@ trait MarkupParser extends MarkupParserCommon with TokenTests {
   protected var curInput: Source = input
 
   // See ticket #3720 for motivations.
-  private class WithLookAhead(underlying: Source) extends Source {
+  // As for why it's `private[parsing]` rather than merely `private`, see
+  // https://github.com/scala/scala-xml/issues/541 ; the broader access is necessary,
+  // for now anyway, to work around https://github.com/lampepfl/dotty/issues/13096
+  private[parsing] class WithLookAhead(underlying: Source) extends Source {
     private val queue = scala.collection.mutable.Queue[Char]()
     def lookahead(): BufferedIterator[Char] = {
       val iter = queue.iterator ++ new Iterator[Char] {