A new criterion for the optimum design of curved dielectric waveguides is proposed. The bends designed according to this model are named matched bends. In the matched bend, the suitable choice of both bending radius and bending angle reduces the total losses of the bend and avoids the leaky-mode excitation at the end of the bend. For a given angle, a discrete number of bending radii that satisfy the matched bend criterion can be analytically determined. With respect to the lateral offset, matched bends are more robust to both fabrication tolerances and wavelength and can be realized in every technology. The reduction of the leaky-mode excitation at the output of the bend is a fundamental property when two or more components are cascaded. Ghost images in the spectral response, cross talk, and asymmetries of the transfer function are successfully reduced. Some examples that use buried, rib, ridge, and diffused waveguides are presented and discussed.