The efficacy of COVID-19 vaccines appears to depend in complex ways on the vaccine dosage and the interval between the prime and boost doses. Unexpectedly, lower dose prime and longer prime-boost intervals have yielded higher efficacies in clinical trials. To elucidate the origins of these effects, we developed a stochastic simulation model of the germinal centre (GC) reaction and predicted the antibody responses elicited by different vaccination protocols. The simulations predicted that a lower dose prime could increase the selection stringency in GCs due to reduced antigen availability, resulting in the selection of GC B cells with higher affinities for the target antigen. The boost could relax this selection stringency and allow the expansion of the higher affinity GC B cells selected, improving the overall response. With a longer dosing interval, the decay in the antigen with time following the prime could further increase the selection stringency, amplifying this effect. The effect remained in our simulations even when new GCs following the boost had to be seeded by memory B cells formed following the prime. These predictions offer a plausible explanation of the observed paradoxical effects of dosage and dosing interval on vaccine efficacy. Tuning the selection stringency in the GCs using prime-boost dosages and dosing intervals as handles may help improve vaccine efficacies.