Trilayer structures, comprising a thin-film In/InO x superconductor separated from an Al gate electrode by an overgrown dielectric, have been studied to ascertain the feasibility of electric-field control of superconductivity for device applications, Modulation of the areal charge density of 50-A thick In/InO x films has been found to cause more than a 350Ω/ box$^b$ change in the sheet resistance near the midpoint of the resistive transition in one film and the creation of ~10Ω/ box$^b$ of resistance from the superconducting state of a second film. We report on efforts to increase this modulation by decreasing the electron density of unperturbed films, improving the charge storage capabilities of the thin-film gate dielectrics, and improving the carrier mobility which has been found to be sensitive to interface preparation. Device implications, based on these results, are also discussed.