Answer set programming (ASP) is a well-established declarative paradigm. One of the successes of ASP is the availability of efficient systems. State-of-the-art systems are based on the ground+solve approach. In some applications, this approach is infeasible because the grounding of one or a few constraints is expensive. In this paper, we systematically compare alternative strategies to avoid the instantiation of problematic constraints, which are based on custom extensions of the solver. Results on real and synthetic benchmarks highlight some strengths and weaknesses of the different strategies.