In Israel, most ancient sites (3000-500 BC) are stratified mounds, i.e., sites to which people returned over and over again. The archaeological method of excavation for such sites is to dig from the top of the mound downward, one stratum at a time, record its architectural components, and subsequently dismantle the remains for the excavation of the next stratum. In recent years a dilemma has arisen. Archaeologists are working mainly with public funds and are expected to leave behind, in situ, authentic architectural remains for the public. Excavation of stratum after stratum will give full knowledge of the site but will leave behind an uninteresting pit. On the other hand the decision to preserve a certain stratum will stop the excavation in that particular site and prevent any further knowledge of the earlier, yet unexcavated strata. Examines several concrete examples and presents possible solutions.