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Two types of low-loss converters between different optical waveguides on silicon-on-insulator are demonstrated. A vertical taper between 9.4- and 3.8-μm-thick single-moded rib waveguides gives an excess loss of 0.7±0.2 dB with negligible polarization dependency. The second structure converts a 9.7-μm-thick rib waveguide into an equally thick and highly multimoded strip waveguide with a negligible loss (<0.07 dB) for the fundamental mode. The fabrication of both structures is based on a simple two-step etch process with a relaxed mask alignment tolerance and no need for epitaxy.