Emacs doesn't interpret down-mouse events on `before' and `after' strings

[Johan Bockgård]

   ;;;
   (setq ov (make-overlay 1 3))
   (setq map (make-sparse-keymap))
   (define-key map [down-mouse-1] 'A)
   (define-key map [mouse-1]      'B)
   (setq str (propertize "XXX" 'keymap map))
   (overlay-put ov 'before-string str)
   (global-set-key [down-mouse-1] 'C)
   (global-set-key [mouse-1]      'D)

M-x eval-buffer

Clicking outside the overlay beeps twice and displays:

  Symbol's function definition is void: C
  Symbol's function definition is void: D

Clicking on the overlay beeps once and displays:

  Symbol's function definition is void: B

What happened to the down-mouse event?

-- 
Johan Bockgård