Gradient masks in flash cs4

Is it possible to get a ‘feathered’ mask in Flash CS4 where the edges of the mask gradually transition to 0 alpha?

I tried to set this up by creating drawing a shape with the pen tool, turning into a movieclip, then filling the original outline with a white (or lime green) center to black on outside, with the outside fading to an alpha value of zero.

When I apply this as a mask, however, the borders are completely sharp rather than the layer below being ‘partially’ masked.

Am I doing something wrong, or can’t you create a feathered mask in Flash CS4?