diff --git a/compiler/src/dotty/tools/dotc/core/Definitions.scala b/compiler/src/dotty/tools/dotc/core/Definitions.scala
index c3b462f3b179..4a48eccffec9 100644
--- a/compiler/src/dotty/tools/dotc/core/Definitions.scala
+++ b/compiler/src/dotty/tools/dotc/core/Definitions.scala
@@ -1620,11 +1620,11 @@ class Definitions {
 
   /** If `cls` is Tuple1..Tuple22, add the corresponding *: type as last parent to `parents` */
   def adjustForTuple(cls: ClassSymbol, tparams: List[TypeSymbol], parents: List[Type]): List[Type] = {
-    def syntheticParent(tparams: List[TypeSymbol]): Type =
-      if (tparams.isEmpty) TupleTypeRef
-      else TypeOps.nestedPairs(tparams.map(_.typeRef))
-    if (isTupleClass(cls)) parents :+ syntheticParent(tparams)
-    else parents
+    if !isTupleClass(cls) then parents
+    else if tparams.isEmpty then parents :+ TupleTypeRef
+    else
+      assert(parents.head.typeSymbol == ObjectClass)
+      TypeOps.nestedPairs(tparams.map(_.typeRef)) :: parents.tail
   }
 
   /** If it is BoxedUnit, remove `java.io.Serializable` from `parents`. */
@@ -1777,6 +1777,7 @@ class Definitions {
       .updated(SingletonClass, ObjectClass)
       .updated(TupleClass, ProductClass)
       .updated(NonEmptyTupleClass, ProductClass)
+      .updated(PairClass, ObjectClass)
 
   // ----- Initialization ---------------------------------------------------
 
diff --git a/tests/neg/i13435.check b/tests/neg/i13435.check
new file mode 100644
index 000000000000..d60bea7ab588
--- /dev/null
+++ b/tests/neg/i13435.check
@@ -0,0 +1,12 @@
+-- [E029] Pattern Match Exhaustivity Warning: tests/neg/i13435.scala:7:2 -----------------------------------------------
+7 |  s match
+  |  ^
+  |  match may not be exhaustive.
+  |
+  |  It would fail on pattern case: (_), ((_, _), (_, _))
+
+longer explanation available when compiling with `-explain`
+-- Error: tests/neg/i13435.scala:8:10 ----------------------------------------------------------------------------------
+8 |    case (dim: Axis, size: Int) => dim // error
+  |          ^^^^^^^^^
+  |          trait Singleton cannot be used in runtime type tests
diff --git a/tests/neg/i13435.scala b/tests/neg/i13435.scala
new file mode 100644
index 000000000000..eaff4976eb71
--- /dev/null
+++ b/tests/neg/i13435.scala
@@ -0,0 +1,8 @@
+type Axis = String&Singleton
+type ShapeTuple = Tuple1[(Axis, Int)]|Tuple2[(Axis, Int), (Axis, Int)]
+type Shape = (Axis, Int) |ShapeTuple
+
+
+def mkSchema(s: Shape) =
+  s match
+    case (dim: Axis, size: Int) => dim // error
\ No newline at end of file