A new method is presented, based on the discrete Fourier Transform, for the design of aperiodic lattices to be used in photonic bandgap engineering. Designing an aperiodic lattice by randomly choosing defects is unlikely to result in useful optical transmission characteristics. By contrast, this new method allows an aperiodic lattice to be designed directly from the desired optical characteristic. The use of this method is illustrated with a design for a structure to realise two transmission wavelengths in the stopband of a one-dimensional photonic lattice. This design has been fabricated in silicon-on-insulator and some optical characteristics are given.