The Anti-de Sitter Space/Conformal Field Theory (AdS/CFT) correspondence may offer new and useful insights into the non-perturbative regime of strongly coupled gauge theories such as Quantum Chromodynamics (QCD). Soft-wall AdS/QCD models have reproduced the linear Regge trajectories of meson spectra by including background dilaton and chiral condensate fields. Efforts to derive these background fields from a scalar potential have so far been unsuccessful in satisfying the UV boundary conditions set by the AdS/CFT dictionary while reproducing the IR behavior needed to obtain the correct meson spectra. We present a three-field scalar potential that includes the dilaton field and the chiral and glueball condensates. This potential is consistent with background fields that yield linear trajectories for the meson spectra and the correct mass-splitting between the vector and axial-vector mesons.