first ... consider trimming the seams to 1/8" and even "layering" so that the fabric on bottom (after it's ironed to one side) is trimmed closer than the fabric that lays on the top. This will allow the top fabric to layer over the bottom and lay flatter.
Do they come together in a point, like a Lone Star? If so, I iron all my seams in the same direction so when they meet in the center - they "fan out" and around in a spiral. There is some bulk - no avoiding that, but it's lessened.