Wu and Sprung (Phys. Rev. E, 48, 2595 (1993)) reproduced the first 500 nontrivial Riemann zeros, using a one-dimensional local potential model. They concluded - as did van Zyl and Hutchinson (Phys. Rev. E, 67, 066211 (2003)) - that the potential possesses a fractal structure of dimension d = 3/2. We model the nonsmooth fluctuating part of the potential by the alternating-sign sine series fractal of Berry and Lewis A(x, gamma). Setting d = 3/2, we estimate the frequency parameter (gamma), plus an overall scaling parameter (sigma) that we introduce. We search for that pair of parameters (gamma, sigma) that minimizes the least-squares fit S-n(gamma, sigma) of the lowest n eigenvalues - obtained by solving the one-dimensional stationary (nonfractal) Schrodinger equation with the trial potential (smooth plus nonsmooth parts) - to the lowest if Riemann zeros for n = 25. For the additional cases, we study, n = 50 and 75, we simply set sigma = 1. The fits obtained are compared to those found by using just the smooth part of the Wu-Sprung potential without any fractal supplementation. Some limited improvement - 5.7261 versus 6.39207 (n = 25), 11.2672 versus 11.7002 (n = 50), and 16.3119 versus 16.6809 (n = 75) - is found in our (nonoptimized, computationally bound) search procedures. The improvements are relatively strong in the vicinities of gamma = 3 and (its square) 9. Further, we extend the Wu-Sprung semiclassical framework to include higher order corrections from the Riemann-von Mangoldt formula (beyond the leading, dominant term) into the smooth potential.