Scala: implementing method with return type of concrete instance

The only solution I could think of was this one:

trait CanCopy[T <: CanCopy[T]] { self: T =>
  type Self >: self.type <: T
  def copy(newId: Int): Self
}

abstract class A(id: Int) { self:CanCopy[_] =>
  def copy(newId: Int): Self
}

The following would compile:

class B(id: Int, x: String) extends A(id) with CanCopy[B] {
  type Self = B
  def copy(newId: Int) = new B(newId, x)
}

class C(id: Int, y: String, z: String) extends A(id) with CanCopy[C] {
  type Self = C
  def copy(newId: Int) = new C(newId, y, z)
}

The following would not compile:

class D(id: Int, w: String) extends A(id) with CanCopy[D] {
  type Self = A
  def copy(newId: Int) = new D(newId, w) // returns an A
}

class E(id: Int, v: String) extends A(id) with CanCopy[E] {
  type Self = B
  def copy(newId: Int) = new B(newId, "")
}

Edit

I actually forgot to remove the copy method. This might be a bit more generic:

trait StrictSelf[T <: StrictSelf[T]] { self: T =>
  type Self >: self.type <: T
}

abstract class A(id: Int) { self:StrictSelf[_] =>
  def copy(newId:Int):Self
}