To maintain tissue homeostasis, some organs are able to replace dying cells with additional proliferation of surviving cells. Such proliferation can be localized (e.g., a regeneration blastema) or diffuse (compensatory growth). The relationship between such growth and the growth that occurs during development has not been characterized in detail. Drosophila melanogaster larval imaginal discs can recover from extensive damage, producing normally sized adult organs. Here we describe a system using genetic mosaics to screen for recessive mutations that impair compensatory growth. By generating clones of cells that carry a temperature-sensitive cell-lethal mutation, we conditionally ablate patches of tissue in the imaginal disc and assess the ability of the surviving sister clones to replace the lost tissue. We have used this system together with a modified whole-genome resequencing (WGS) strategy to identify several mutations that selectively compromise compensatory growth. We find specific alleles of bunched (bun) and Ribonucleoside diphosphate reductase large subunit (RnrL) reduce compensatory growth in the imaginal disc. Other genes identified in the screen, including two alleles of Topoisomerase 3-alpha (Top3α), while also required for developmental growth, appear to have an enhanced requirement during compensatory growth. Compensatory growth occurs at a higher rate than normal growth and may therefore have features in common with some types of overgrowth. Indeed, the RnrL allele identified compromises both these types of altered growth and mammalian ribonucleotide reductase and topoisomerases are targets of anticancer drugs. Finally, the approach we describe is applicable to the study of compensatory growth in diverse tissues in Drosophila.