To test the accuracy of various methods previously proposed (and one new method) to estimate offence times where the actual time of the event is not known. For 303 thefts of pedal cycles from railway stations, the actual offence time was determined from closed-circuit television and the resulting temporal distribution compared against commonly-used estimated distributions using circular statistics and analysis of residuals. Aoristic analysis and allocation of a random time to each offence allow accurate estimation of peak offence times. Commonly-used deterministic methods were found to be inaccurate and to produce misleading results. It is important that analysts use the most accurate methods for temporal distribution approximation to ensure any resource decisions made on the basis of peak times are reliable.