diff --git a/compiler/src/dotty/tools/dotc/core/TypeComparer.scala b/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
index ca5059c944c6..fa84b914a561 100644
--- a/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
+++ b/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
@@ -2881,6 +2881,12 @@ class TypeComparer(@constructorOnly initctx: Context) extends ConstraintHandling
         true
       case (_, _: HKLambda) =>
         true
+      /* Nothing is not a class type in the spec but dotc represents it as if it were one.
+       * Get it out of the way early to avoid mistakes (see for example #20897).
+       * Nothing ⋔ T and T ⋔ Nothing for all T.
+       */
+      case (tp1, tp2) if tp1.isExactlyNothing || tp2.isExactlyNothing =>
+        true
       case (tp1: OrType, _)  =>
         provablyDisjoint(tp1.tp1, tp2) && provablyDisjoint(tp1.tp2, tp2)
       case (_, tp2: OrType)  =>
@@ -2891,6 +2897,12 @@ class TypeComparer(@constructorOnly initctx: Context) extends ConstraintHandling
       case (_, tp2: AndType) =>
         !(tp2 <:< tp1)
         && (provablyDisjoint(tp1, tp2.tp2) || provablyDisjoint(tp1, tp2.tp1))
+      /* Handle AnyKind now for the same reason as Nothing above: it is not a real class type.
+       * Other than the rules with Nothing, unions and intersections, there is structurally
+       * no rule such that AnyKind ⋔ T or T ⋔ AnyKind for any T.
+       */
+      case (tp1, tp2) if tp1.isDirectRef(AnyKindClass) || tp2.isDirectRef(AnyKindClass) =>
+        false
       case (tp1: NamedType, _) if gadtBounds(tp1.symbol) != null =>
         provablyDisjoint(gadtBounds(tp1.symbol).uncheckedNN.hi, tp2)
         || provablyDisjoint(tp1.superTypeNormalized, tp2)
diff --git a/compiler/test/dotc/pos-test-pickling.blacklist b/compiler/test/dotc/pos-test-pickling.blacklist
index fd40d8b3577a..8293d0a69d79 100644
--- a/compiler/test/dotc/pos-test-pickling.blacklist
+++ b/compiler/test/dotc/pos-test-pickling.blacklist
@@ -57,6 +57,7 @@ i15158.scala
 i15155.scala
 i15827.scala
 i18211.scala
+i20897.scala
 
 # Opaque type
 i5720.scala
@@ -112,4 +113,3 @@ i15525.scala
 i19955a.scala
 i19955b.scala
 i20053b.scala
-
diff --git a/tests/pos/i20897.scala b/tests/pos/i20897.scala
new file mode 100644
index 000000000000..ecfac5b1615e
--- /dev/null
+++ b/tests/pos/i20897.scala
@@ -0,0 +1,10 @@
+object Test:
+  type Disj[A, B] =
+    A match
+      case B => true
+      case _ => false
+
+  def f(a: Disj[1 | Nothing, 2 | Nothing]): Unit = ()
+
+  val t = f(false)
+end Test