Approaches to photon event counting imaging in which the output events of an image intensifier are located using a centroiding technique have long been plagued by fixed pattern noise in which a grid of dimensions similar to those of the CCD pixels is superimposed on the image. This is caused by a mismatch between the photon event shape and the centroiding algorithm. We have used hyperbolic cosine, Gaussian, Lorentzian, parabolic as well as 3-, 5-, and 7-point centre of gravity algorithms, and hybrids thereof, to assess means of minimising this fixed pattern noise. We show that fixed pattern noise generated by the widely used centre of gravity centroiding is due to intrinsic features of the algorithm. Our results confirm that the recently proposed use of Gaussian centroiding does indeed show a significant reduction of fixed pattern noise compared to centre of gravity centroiding (Michel et al., Mon. Not. R. Astron. Soc. 292 (1997) 611-620). However, the disadvantage of a Gaussian algorithm is a centroiding failure for small pulses, caused by a division by zero, which leads to a loss of detective quantum efficiency (DQE) and to small amounts of residual fixed pattern noise. Using both real data from an image intensifier system employing a progressive scan camera, framegrabber and PC, and also synthetic data from Monte-Carlo simulations, we find that hybrid centroiding algorithms can reduce the fixed pattern noise without loss of resolution or loss of DQE. Imaging a test pattern to assess the features of the different algorithms shows that a hybrid of Gaussian and 3-point centre of gravity centroiding algorithms results in an optimum combination of low fixed pattern noise (lower than a simple Gaussian), high DQE, and high resolution. The Lorentzian algorithm gives the worst results in terms of high fixed pattern noise and low resolution, and the Gaussian and hyperbolic cosine algorithms have the lowest DQEs.