A method for correcting integrating-sphere signals that considers differences in the angular distribution of scattered light is extended to sources of errors that are due to stray light from imperfect optical components. We show that it is possible to measure low levels of scattering, below 1%, by using a standard integrating sphere, provided that the various contributions to stray light are taken into account properly. For low-scattering samples these corrections are more important than those from the angular distribution of the scattering. A procedure for the experimental determination of stray-light components is suggested. Simple, easy to use, compact equations for the diffuse and specular reflectance and transmittance values of the sample as functions of the recorded signals are presented.