We study small field inflationary models that can generate a significant Gravitational Wave (GW) signal while producing CMB observables that conform to current experimental values. To this end, we have created a stand-alone numerical simulator that, given an inflationary potential, yields the associated Primordial Power Spectrum (PPS). We found a discrepancy between the results of analytical evaluation methods of the PPS and numerical calculations. We present our models and discuss their theoretical merit. The numerical code is then outlined. We first demonstrate the ability to cover the currently allowed observable parameter space with models that produce a significant GW at the level of r=0.03. We then show a disparity between numerical computation and analytical predictions in our models. We discuss some of the possible reasons for this inadequacy of pure analytics and conclude.