Estimating the level of sexual victimization is problematic. Crimes recorded by the police routinely undercount sexual offenses, primarily because few victims report their victimization to the police. Crime (or victimization) surveys in principle promise a more complete count, but in practice survey measures have left much to be desired. The BCS has covered sexual victimization in all of its "sweeps," using conventional techniques. In an attempt to improve measurements, an innovative self-completion component was introduced in the 1994 BCS; women used computers to read and answer questions. The core of this paper reports on this methodology and its results, including those from an unusual question about the sexual incidents the women reported in the interview. Also described are the measurement techniques adopted in the NCVS before and after its redesign, as well as the techniques for collecting data on sexual offenses in the VAWS and the ICS. The discussion focuses on the wide range in estimates of sexual offenses among the surveys. The conclusion outlines some measurement issues based on the assessment of the victimization surveys. 12 tables and 58 references