We report a simple ad hoc method for designing an aperiodic grating structure to quasi-phase match two arbitrary second-order nonlinear processes simultaneously within the same electric-field-poled crystal. This method also allows the relative strength of the two processes to be adjusted freely, thereby enabling maximization of the overall conversion efficiency. We also report an experiment that is based on an aperiodically poled lithium niobate crystal that was designed by use of our method. In this crystal, parametric oscillation and second-harmonic generation are simultaneously phase matched for upconversion of a femtosecond Ti:sapphire laser to 570 nm. This self-doubling optical parametric oscillator provides an experimental verification of our design method. © 2003 Optical Society of America.