We investigate the influence of different chemical and physical processes on the water vapour distribution in the lower stratosphere (LS), in particular in the Asian and North American monsoon anticyclones (AMA and NAMA, respectively). Specifically, we use the chemistry transport model CLaMS to analyse the effects of large-scale temperatures, methane oxidation, ice microphysics, and small-scale atmospheric mixing processes in different model experiments. All these processes hydrate the LS and, particularly, the AMA. While ice microphysics has the largest global moistening impact, it is small-scale mixing which dominates the specific signature in the AMA in the model experiments. In particular, the small-scale mixing parameterization strongly contributes to the water vapour transport to this region and improves the simulation of the intra-seasonal variability, resulting in a better agreement with the Aura Microwave Limb Sounder (MLS) observations. Although none of our experiments reproduces the spatial pattern of the NAMA as seen in MLS observations, they all exhibit a realistic annual cycle and intra-seasonal variability, which are mainly controlled by large-scale temperatures. We further analyse the sensitivity of these results to the domain-filling trajectory set-up, here-called Lagrangian trajectory filling (LTF). Compared with MLS observations and with a multiyear reference simulation using the full-blown chemistry transport model version of CLaMS, we find that the LTF schemes result in a drier global LS and in a weaker water vapour signal over the monsoon regions, which is likely related to the specification of the lower boundary condition. Overall, our results emphasize the importance of subgrid-scale mixing and multiple transport pathways from the troposphere in representing water vapour in the AMA.