Several approaches exist to use trends in 3D seismic data, in the form of seismic attributes, to interpolate sparsely sampled well-log measurements between well locations. Kriging and neural networks are two such approaches. We have applied a method that finds a relation between seismic attributes (such as two-way times, interval velocities, reflector roughness) and rock properties (in this case, acoustic impedance) from information at well locations. The relation is designed for optimum prediction of acoustic impedances away from well sites, and this is accomplished through a combination of cross validation and the Tikhonov-regularized least-squares method. The method is fast, works well even for highly underdetermined problems, and has general applicability. We apply it to two case studies in which we estimate 3D cubes of low-frequency impedance, which is essential for producing good porosity models. We show that the method is superior to traditional least squares: Numerous blind tests show that estimated low-frequency impedance away from well locations can be determined with an accuracy very close to estimations obtained at well locations.