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^-1 s^-1.