In this paper, the oxidation of thin low-Sb-containing AlAsSb layers quasi-lattice matched on GaAs substrates is studied in detail since, compared to AlGaAs, these alloys had the prospects of being laterally oxidized at a faster rate, at lower process temperatures and with a reduced volume change. Combining monitoring data of the oxidation kinetics and anisotropy with atomic-force-microscopy surface measurements enables to establish the optimal composition range and process parameters that lead to nearly-isotropic and Sb-segregation-free oxidations. The study also shows that strain plays a central role in triggering the detrimental Sb segregation.