I will discuss recent joint work with R. Sullivan and J. Winkel where we show the simplicity of the automorphism groups of several homogeneous structures: most notably the generic n-hypertournament and the dense local order S_2. The novelty here is that previous results of Macpherson, Tent and Ziegler (generalised to the asymmetric case by Li) do not immediately apply, as the structures concerned do not have a suitable independence relation. We get around this difficulty by extending a trick involving pointwise stabilisers found in an article of Macpherson.