When direct methods for solving large, sparse, nonsymmetric systems of linear equations use too much computer memory, users often turn to preconditioned iterative methods. It can be critical in solving such systems to choose a preconditioner which both uses a limited amount of memory, and helps the subsequently applied iterative solver converge more rapidly. This paper describes ILUTP_Mem, an incomplete LU preconditioner that computes an incomplete LU factorization that effectively uses an amount of space specified by the user. The ILUTP_Mem preconditioner is evaluated on a set of matrices from real applications.