  In this paper we discuss in detail an experimental scheme to test the
universality of free fall (UFF) with a differential $^{87}$Rb / $^{85}$Rb atom
interferometer applicable for extended free fall of several seconds in the
frame of the STE-QUEST mission. This analysis focuses on suppression of noise
and error sources which would limit the accuracy of a violation measurement. We
show that the choice of atomic species and the correctly matched parameters of
the interferometer sequence are of utmost importance to suppress leading order
phase shifts. In conclusion we will show the expected performance of $2$ parts
in $10^{15}$ of such an interferometer for a test of the UFF.
