Novelty search is a recent algorithm geared toward exploring search spaces without regard to objectives. When the presence of constraints divides a search space into feasible space and infeasible space, interesting implications arise regarding how novelty search explores such spaces. This paper elaborates on the problem of constrained novelty search and proposes two novelty search algorithms which search within both the feasible and the infeasible space. Inspired by the FI-2pop genetic algorithm, both algorithms maintain and evolve two separate populations, one with feasible and one with infeasible individuals, while each population can use its own selection method. The proposed algorithms are applied to the problem of generating diverse but playable game levels, which is representative of the larger problem of procedural game content generation. Results show that the two-population constrained novelty search methods can create, under certain conditions, larger and more diverse sets of feasible game levels than current methods of novelty search, whether constrained or unconstrained. However, the best algorithm is contingent on the particularities of the search space and the genetic operators used. Additionally, the proposed enhancement of offspring boosting is shown to enhance performance in all cases of two-population novelty search.