ABSTRACT The claimed detection of large amounts of substructure in lensing flux anomalies, and in Milky Way stellar stream gap statistics, has led to a step change in constraints on simple warm dark matter models. In this study, we compute predictions for the halo mass function both for these simple models and for comprehensive particle physics models of sterile neutrinos and dark acoustic oscillations. We show that the mass function fit of Lovell et al. underestimates the number of haloes less massive than the half-mode mass, $M_\mathrm {hm}$, by a factor of 2, relative to the extended Press–Schechter (EPS) method. The alternative approach of applying EPS to the Viel et al. matter power spectrum fit instead suggests good agreement at $M_\mathrm {hm}$ relative to the comprehensive model matter power spectrum results, although the number of haloes with mass $\rm{\lt} M_\mathrm {hm}$ is still suppressed due to the absence of small-scale power in the fitting function. Overall, we find that the number of dark matter haloes with masses $\rm{\lt} 10^{8}{\, \rm M_⊙ }$ predicted by competitive particle physics models is underestimated by a factor of ∼2 when applying popular fitting functions, although careful studies that follow the stripping and destruction of subhaloes will be required in order to draw robust conclusions.