Novelty search is a recent algorithm geared to explore search spaces without regard to objectives; minimal criteria novelty search is a variant of this algorithm for constrained search spaces. For large search spaces with multiple constraints, however, it is hard to find a set of feasible individuals that is both large and diverse. In this paper, we present two new methods of novelty search for constrained spaces, Feasible-Infeasible Novelty Search and Feasible-Infeasible Dual Novelty Search. Both algorithms keep separate populations of feasible and infeasible individuals, inspired by the FI-2pop genetic algorithm. These algorithms are applied to the problem of creating diverse and feasible game levels, representative of a large class of im...