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Determination of the spin-exchange rate coefficients between Xe nuclei and alkali-metal atoms is complicated due to various mechanisms of spin-exchange as formation and destruction of van der Waals molecules and binary collisions. There are a variety of conflicting measurements in the literature, recently reviewed by Kelley and Branca. Measurements that rely on temperature dependences are potentially ambiguous due to the difficulty of isolating wall relaxation from the other processes. We will summarize different methods for measuring spin-exchange rate coefficient without making assumptions about wall relaxation and we will present preliminary measurements of the Rb-Xe spin-exchange rate coefficient under typical conditions used in NMR gyroscopes.