Compensatory growth where animals compensate for time stress or transient nutritional or thermal stress by accelerating their growth rate is widespread. We know, however, relatively little about the evolution and ecological correlates of compensatory growth. For this we need studies on congeneric species with known phylogenetic relationships that also focus on the associated largely understudied costs. Here we tested for compensatory growth and associated costs in response to time stress (manipulated by photoperiod) and a transient period of starvation or cooling in larvae of the permanent-pond damselfly Lestes eurinus, and compare the results with former studies on temporary-pond Lestes. Larvae showed full compensation in body mass at emergence for all combinations of time stress and starvation or cooling. Unexpectedly, compensatory growth to starvation or cooling was not stronger under time stress. Instead, males under time stress delayed emergence after these transient stressors. In line with a stronger compensatory growth response to time stress than to the other stressors, physiological costs in terms of a reduced investment in immune response (measured as phenoloxidase activity) and energy storage (measured as fat content) were detected only under time stress. Compared to temporary-pond Lestes, L. eurinus showed stronger compensatory growth to time stress. We hypothesize that the stronger compensatory (growth) response in permanent-pond Lestes co-evolved with their derived slower lifestyle when they invaded permanent ponds.