The determination of heavy element abundances from planetary nebula (PN) spectra provides an exciting opportunity to study the nucleosynthesis occurring in the progenitor asymptotic giant branch (AGB) star. We perform post-processing calculations on AGB models of a large range of mass and metallicity to obtain predictions for the production of neutron-capture elements up to the first s-process peak at strontium. We find that solar metallicity intermediate-mass AGB models provide a reasonable match to the heavy element composition of Type I PNe. Likewise, many of the Se and Kr enriched PNe are well fitted by lower mass models with solar or close-to-solar metallicities. However, those objects most enriched in Krand those PN with sub-solar Se/O ratios are difficult to explain with AGB-nucleosynthesis models. Furthermore, we compute s-process abundance predictions for low-mass AGB models of very low metallicity ([Fe/H]≈−2.3) using both scaled solar and an α-enhanced initial composition. For these models, O is dredged to the surface, which means that abundance ratios measured relative to this element (e.g. X/O) do not provide a reliable measure of initial abundance ratios, or of production within the star owing to internal nucleosynthesis.