you might be able to do a color to alpha operation a number of time with gradients, getting the end color values of the gradient.
say the gradient goes from red to orange, you'd color to alpha red, and color to alpha orange, again with the selection techniques or else you could forget up your image turning it from purple to green or something.
by selection techniques, i mean just making a selection around the object, inverting the selection so it selects everything around the object, and then growing it by 1 pixel so that the selection encompasses the object more, including it's white edges to be transed because otherwise because of gimp's selection threshold it'll only trans everything just outside the white edges as if you just selected and pressed delete in paint.net.
in some cases it'd be a good idea to feather the selection for that smoother edge, but not too much.