Genetic programming systems often use large training sets to evaluate the quality of candidate solutions for selection, which is often computationally expensive. Down-sampling training sets has long been used to decrease the computational cost of evaluation in a wide range of application domains. More specifically, recent studies have shown that both random and informed down-sampling can substantially improve problem-solving success for GP systems that use the lexicase parent selection algorithm. We test whether these down-sampling techniques can also improve problem-solving success in the context of three other commonly used selection methods, fitness-proportionate, tournament, implicit fitness sharing plus tournament selection, across six program synthesis GP problems. We verified that down-sampling can significantly improve the problem-solving success for all three of these other selection schemes, demonstrating its general efficacy. We discern that the selection pressure imposed by the selection scheme does not interact with the down-sampling method. However, we find that informed down-sampling can improve problem solving success significantly over random down-sampling when the selection scheme has a mechanism for diversity maintenance like lexicase or implicit fitness sharing. Overall, our results suggest that down-sampling should be considered more often when solving test-based problems, regardless of the selection scheme in use.