We have used time resolved spectroscopy to measure the relaxation of spin polarization in InSb/AlInSb quantum wells (QWs) as a function of temperature and mobility. The results are consistent with the D'yakonov-Perel (DP) mechanism for high mobility samples over the temperature range from 50 to 300 K. For low mobility samples at high temperature the Elliott-Yafet and DP mechanisms become comparable. We show that the mobility can in certain circumstances determine which mechanism is dominant, and that above 1 m2 V-1 s-1 in 20 nm wide InSb QWs it is the DP mechanism. We also give a criterion for the maximum spin lifetime in terms of mobility and temperature, and show that for our 20 nm wide QWs this corresponds to 0.5 ps at 300 K and mobility 1 m2 V-1s-1. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.