The development of a practical approach to higher order generalized perturbation theory (GPT) methods is documented. The method combines a direct correlation technique for obtaining a first-order estimate of the perturbed flux distribution with an explicit representation of second-order GPT for obtaining improved predictions of perturbed integral responses. The technique is easy to use and it does not require extensive methods development efforts; it simply relies on the manipulation of data from several direct perturbation runs and several adjoint computations (and this step can be fully automated). Demonstration cases using a pressurized water reactor benchmark model have verified the adequacy of the method for improving the practicality of using GPT in design applications. The best success to date has been for cases where only a few large localized variations are made. When changes are made at several locations throughout the model, the cancellation of large positive and negative effects tends to introduce increased error in the flux estimates. Current efforts are focused on methods to mitigate some of this numerical cancellation. Overall, the method shows good promise for improving on the use of first-order GPT for application to the core reload design problem.