diff --git a/compiler/src/dotty/tools/dotc/typer/Namer.scala b/compiler/src/dotty/tools/dotc/typer/Namer.scala
index 02a55be9ea5a..fc7067c7b45e 100644
--- a/compiler/src/dotty/tools/dotc/typer/Namer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Namer.scala
@@ -995,8 +995,12 @@ class Namer { typer: Typer =>
       end if
     }
 
+    /** Imply `update` for consume methods in Mutable classes */
     private def normalizeFlags(denot: SymDenotation)(using Context): Unit =
-      if denot.is(Method) && denot.hasAnnotation(defn.ConsumeAnnot) then
+      if denot.is(Method)
+          && denot.hasAnnotation(defn.ConsumeAnnot)
+          && denot.owner.derivesFrom(defn.Caps_Mutable)
+      then
         denot.setFlag(Mutable)
 
     /** Intentionally left without `using Context` parameter. We need
diff --git a/docs/_docs/reference/experimental/capture-checking/separation-checking.md b/docs/_docs/reference/experimental/capture-checking/separation-checking.md
index 7fcb35658679..52b80a9e5782 100644
--- a/docs/_docs/reference/experimental/capture-checking/separation-checking.md
+++ b/docs/_docs/reference/experimental/capture-checking/separation-checking.md
@@ -195,7 +195,7 @@ Buffers in Scala's standard library use a single-argument method `+=` instead of
 class Buffer[T] extends Mutable:
   consume def +=(x: T): Buffer[T]^ = this // ok
 ```
-`consume` on a method implies `update`, so there's no need to label `+=` separately as an update method. Then we can write
+`consume` on a method in a `Mutable` class implies `update`, so there's no need to label `+=` separately as an update method. Then we can write
 ```scala
 val b = Buffer[Int]() += 1 += 2
 val c = b += 3
diff --git a/tests/pos-custom-args/captures/i24372.scala b/tests/pos-custom-args/captures/i24372.scala
new file mode 100644
index 000000000000..76c3d85e08fe
--- /dev/null
+++ b/tests/pos-custom-args/captures/i24372.scala
@@ -0,0 +1,2 @@
+trait Foo extends caps.ExclusiveCapability:
+  consume def sink: Unit = ()