We present a new method for modeling the hadronic recoil in W->lnu events produced at hadron colliders. The recoil is chosen from a library of recoils in Z->ll data events and overlaid on a simulated W->lnu event. Implementation of this method requires that the data recoil library describe the properties of the measured recoil as a function of the true, rather than the measured, transverse momentum of the boson. We address this issue using a multidimensional Bayesian unfolding technique. We estimate the statistical and systematic uncertainties from this method for the W boson mass and width measurements assuming 1 fb-1 of data from the Fermilab Tevatron. The uncertainties are found to be small and comparable to those of a more traditional parameterized recoil model. For the high precision measurements that will be possible with data from Run II of the Fermilab Tevatron and from the CERN LHC, the method presented in this paper may be advantageous, since it does not require an understanding of the measured recoil from first principles.