This letter considers the signal design problems for quaternary digital communications with nonuniform sources. The designs are considered for both the average and equal energy constraints and for a two-dimensional signal space. A tight upper bound on the bit error probability (BEP) is employed as the design criterion. The optimal quarternary signal sets are presented and their BEP performance is compared with that of the standard QPSK and the binary signal set previously designed for nonuniform sources. Results shows that a considerable saving in the transmitted power can be achieved by the proposed average-energy signal set for a highly nonuniform source.