Integration of optical functions promises to be an important new technology, with applications in telecommunications, datacommunications, and sensing. Controlling the polarization in integrated circuits is needed to fully benefit from the use of light. Integrated polarization converters are required for this, but devices proposed so far have suffered from tight fabrication tolerances. It is shown here what the root of this intolerance is and how critical fabrication errors can be compensated in a two-section polarization converter. The new device leads to doubling of the fabrication tolerances and wavelength range and promises conversion efficiencies above 99% over a wide range of fabrication and operation parameters.