Resistance distributions for the reset state in phase-change-memory arrays are studied as a function of the programming conditions. The statistical distribution displays a low-resistance tail, which may potentially affect the resistance window between the two states in the memory device. The majority of tail cells are found to result from the statistical dispersion of the quenching properties of the chalcogenide material and can be corrected by optimizing the programming operation. On the other hand, a residual tail is found, which is characterized in terms of programming, switching, and conducting characteristics. The measured behavior is consistent with extrinsic low-resistance paths in the programmable volume, which shunts the high-resistance amorphous phase and prevents reaching a fully reset resistance. Removal of this extrinsic tail in the reset distribution is demonstrated by careful optimization of the integration process.