ActionScript 3.0 :: Creating Bitmap Representation Of Stage?

So, I want to create an effect such that each frame I :
1 ) create a bitmap representation of the stage.
2 ) reduce the bitmap's alpha to .75
3 ) remove any currently existing bitmap from stage
3 ) add new bitmap to stage.

If I'm correct in my thinking, this should effectively create the illusion that the stage is fading over time, as every time you call bitmapData.draw() the bitmap will be set at .75 alpha. This *should* mean that when I apply .75 alpha to the new bitmap that it should effectively result in a new image that is .75 * .75 alpha (.56), then on the next frame again it should be lower still (.42), and on... .31, .23, .17, and so on... But it seems that what's *actually* happening is that the new bitmap always *looks* like it's .75 alpha every frame.

ActionScript Code:
import flash.events.*;
import flash.display.*;
// draw a black box...
this.graphics.beginFill(0x000000);
this.graphics.drawRect(0,0,100,100);
this.graphics.endFill();
[Code] .....

Additionally, I've tried using stage.invalidate and doing parts of this in an Event.RENDER handler, but it didn't work either...