We derive an exact likelihood for data collected using the response-selective stratified sampling (RSSS) design. We discuss the asymptotic properties of the corresponding maximum likelihood estimators, and revise the so-called empirical proportion (EP) likelihood approach to provide consistent and efficient estimation. We propose a “common sample principle" to support the generality of our exact likelihood approach as well as the improved EP likelihood approach, and also enhance the robustness of these likelihood approaches for dealing with the complexity of some realistic sampling designs. Simulation studies show that these two approaches we propose perform better than the existing estimation methods in RSSS. The approaches are illustrated with a case study involving American plaice off the east coast of Canada. This application also involves between-individual variation in growth and covariate measurement error in age.