My Pie slices are "bleeding" - lines too thick

See the attached screenshot for what is happening (which I knew is what would happen) When the line thickness get’s thick, you start noticing that it overwrites the lines for the other slices.

Here is what I **could **do:
Make the line thickness twice as big. When I’m done drawing the graphic, I could draw a second shape after the one I just drew, but this one whithout any line thickness, and use this one as a mask for my original pie slice.

But obviously that is not worth the speed or hassle. Also, I don’t have access to the Mask of the object, only the Graphics class.

Is there any quick way to manually tell the graphics class to keep all lines “inside” of the filled area, instead of just right on the borders, bleeding over the edges?