We explore some algorithms to construct designs for foundation paper piecing. The input is a block consisting of multiple polygonal regions, and the output is a way to split the block into sections and each section into pieces, such that each section is foundation paper pieceable, and also the block is foundation paper pieceable from the sections. The output is accompanied by the order in which its pieces and sections must be sewn together. In particular, it is interesting that every design can be made foundation paper pieceable in at most two stages. We consider various criteria to optimize designs.