Since it's excess fabric, what I usually do in a situation like this is simply re-sew seams in the area of fullness -- starting somewhere towards the middle right on top of the existing seam, then tapering so there is more fabric taken up at the edge. You would want to do this with multiple seams. If you have 1 inch of excess fullness at the edge, then you would want to sew on top of perhaps 4 seams -- making each seam 1/8th inch wider at the edge (which will result in 1/4" less fabric at the edge).
When there is not enough fabric at the edge, you do have to rip before re-sewing. However, when there is excess fabric at the edge, you can simply sew on top of the existing seam and press. No one will know there is extra sewing inside that pressed seam!