Two selection statistics are used to extract new candidate periodic variables from the epoch photometry of the Hipparcos catalogue. The primary selection criterion is a signal-to-noise ratio. The dependence of this statistic on the number of observations is calibrated using about 30000 randomly permuted Hipparcos data sets. A significance level of 0.1 per cent is used to extract a first batch of candidate variables. The second criterion requires that the optimal frequency be unaffected if the data are de-trended by low-order polynomials. We find 2675 new candidate periodic variables, of which the majority (2082) are from the Hipparcos unsolved variables. Potential problems with the interpretation of the data (e.g. aliasing) are discussed.