A recent analysis of gamma rays from the centre of our galaxy has provided possible evidence for a dark matter annihilation signal, with the dark matter taking the form of low-mass WIMPs annihilating predominantly to taus. We study an extended Higgs model proposed to yield such a dark matter candidate. Scanning over parameter space in this model, we find suitable areas that feature fairly little fine-tuning. In favoured areas, the cross-sections for invisible decays of...