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no Condition in EventHandler?

 ("MouseDown" :> Print[1]) /; CurrentValue["AltKey"],
 ("MouseDown" :> Print[2]) /; CurrentValue["ControlKey"],
 ("MouseDown" :> Print[3]) /; CurrentValue["ShiftKey"],
 ("MouseDown" :>
    Print[4, CurrentValue["AltKey"], CurrentValue["ControlKey"],
     CurrentValue["ShiftKey"]]) /; True,
 "MouseDown" :>
  Print[5, CurrentValue["AltKey"], CurrentValue["ControlKey"],
    CurrentValue["ShiftKey"]] /; False

Does not do what I expect.  (5 is always printed, and nothing else, no
matter what keys are down).

I can only speculate that EventHandler doesn't evaluate its actions in
such a way that a Condition has a chance to take effect or not?

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