In γ-ray astronomy one often wishes to search for a periodic signal from a suspected point source. Either one knows the period in advance, for example in the case of a radio pulsar, or at least a range of possible periods, or one has no information and is searching “blind”, as in the case of SN1987a, unidentified sources in the COS-B catalogue, or binary X-ray sources without known pulse periods. In both cases one should adopt a strategy which give the best chance of obtaining a statistically significant result. The power of tests using the family of statistics based on the Rayleigh statistic is discussed for two extreme forms of possible light curves: a uniform distribution plus a delta function, and a cartoid distribution. Strategies for using these statistics are discussed. Methods of obtaining confidence bands, and in the case of an unsuccessful search, upper-limits to any pulsed component are described, and graphs given which enable these to be calculated readily given the value of the statistic obtained.