Irregular waveguide elements in a silicon-on-insulator platform that allow new device concepts are introduced. Specific designs are achieved using a multiresolution optimization strategy where the waveguide width is varied in stepwise increments. Simulation results are given for high-efficiency waveguide mode converters, power splitters, and waveguide transitions operating at 1.55 microm. The degrees of freedom available permit these functions and small dimensions, making these devices candidates for optical integrated circuits.