The purpose of this experiment was to find out how a population becomes adapted to extremely stressful conditions as its environment deteriorates. We created a deteriorating environment for experimental selection lines of yeast by a stepwise increase in the concentration of salt in the growth medium. After each step, we tested the ability of the lines to grow at a high concentration of salt near the lethal limit for the ancestral strain. We found that mutations enhancing growth in this highly stressful environment began to spread at intermediate salt concentrations. The degree of enhancement was related to effective population size by a power law with a small exponent. The effect size of these mutations also increased with the population size in a similar fashion. From these results, we interpret adaptation to lethal stress as an indirect response to selection for resistance to previous lower levels of stress in a deteriorating environment. This suggests that the pattern of genetic correlation between successively higher levels of stress is an important factor in facilitating evolutionary rescue.