We propose new methods for using contracted basis functions in conjunction with the Lanczos algorithm to calculate vibrational (or rovibrational) spectra. As basis functions we use products of eigenfunctions of reduced-dimension Hamiltonians obtained by freezing coordinates at equilibrium. The basis functions represent the desired wave functions well, yet are simple enough that matrix-vector products may be evaluated efficiently. The methods we suggest obviate the need to transform from the contracted to an original product basis each time a matrix-vector product is evaluated. For HOOH the most efficient of the methods we present is about an order of magnitude faster than a product basis Lanczos calculation.