Overlapping or overlaying images, while keeping handlers independent

I'm trying to use one image as a base image, on which I have multiple
smaller images that may or may not overlap, each with a unique mouse-
enter handler.

I heard using AbsolutePanel can allow me to choose an absolute
position on the page to place my images, but overlapping images will
inherit any handlers.

Any way to do what I want to do without meshing together of the
handlers themselves?

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