The iterative reconstruction algorithms employed in brain single-photon emission computed tomography (SPECT) allow some quantitative parameters of the image to be improved. These algorithms require accurate modelling of the so-called point spread function (PSF). Nowadays, most in vivo neurotransmitter SPECT studies employ pharmaceuticals radiolabelled with ¹²³I. In addition to an intense line at 159 keV, the decay scheme of this radioisotope includes some higher energy gammas which may have a non-negligible contribution to the PSF. The aim of this work is to study this contribution for two low-energy high-resolution collimator configurations, namely, the parallel and the fan beam. The transport of radiation through the material system is simulated with the Monte Carlo code PENELOPE. We have developed a main program that deals with the intricacies associated with tracking photon trajectories through the geometry of the collimator and detection systems. The simulated PSFs are partly validated with a set of experimental measurements that use the 511 keV annihilation photons emitted by a ¹⁸F source. Sensitivity and spatial resolution have been studied, showing that a significant fraction of the detection events in the energy window centred at 159 keV (up to approximately 49% for the parallel collimator) are originated by higher energy gamma rays, which contribute to the spatial profile of the PSF mostly outside the 'geometrical' region dominated by the low-energy photons. Therefore, these high-energy counts are to be considered as noise, a fact that should be taken into account when modelling PSFs for reconstruction algorithms. We also show that the fan beam collimator gives higher signal-to-noise ratios than the parallel collimator for all the source positions analysed.