An exact integral relation between the solutions of the Helmholtz and parabolic equations and its stationary phase evaluation has been previously reported [J. A. DeSanto, J. Acoust. Soc. Am. 60, S33 (A) (1976)]. The procedure yields corrections to the parabolic solution (P) which (among others) involve the second range derivative of P. We have programmed this latter correction using the (range-independent) AESD profiles and make a quantitative comparison (rms error as a function of range) between the exact normal mode (NM) result and P, on the one hand, and between NM and the corrected parabolic (CP) on the other. The improvement is dramatic. The rms errors (both including and excluding phase) of the NMCP comparison are at least a factor of 3 less than the NM-P errors. We illustrate the conclusions with extensive numerical results. To summarize: (a) the correction is functionally simple, (b) it's easy to program, and (e) it yields significantly improved results. Finally we remark that the quantitative comparison between propgation models is far better than the canonical eyeball method.