In phase-change materials, the amorphous state resistivity increases with time following a power law q/(t/t0)aRD. This drift in resistivity seriously hampers the potential of multilevel-storage to achieve an increased capacity in phase-change memories. This paper presents the stoichiometric dependence of drift phenomena in amorphous GeSnTe systems (a-GeSnTe) and other known phase-change alloys with the objective to identify low drift materials. The substitution of Ge by Sn results in a systematic decrease of the drift parameter from a-GeTe (alphaRD=0.129) to a-Ge2Sn2Te4 (alphaRD=0.053). Furthermore, with increasing Sn content a decrease in crystallization temperature, trap state density, optical band gap, and activation energy for electronic conduction is observed. In a-GeSnTe, a-GeSbTe, and a-AgInSbTe alloys as well, the drift parameter alphaRD correlates to the activation energy for electronic conduction. This study indicates that low drift materials are characterized by low activation energies of electronic conduction. The correlation found between drift and activation energy of electronic conduction manifests a useful criterion for material optimization.