Properties of the free-energy landscape in phase space of a dense hard-sphere system characterized by a discretized free-energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local minima of the free energy are located and the distribution of an appropriately defined overlap' between minima is calculated. The process of transition from the basin of attraction of a minimum to that of another one is studied using a new microcanonical' Monte Carlo procedure, leading to a determination of the effective height of free-energy barriers that separate different glassy minima. The general appearance of the free-energy landscape resembles that of a putting green: deep minima separated by a fairly Rat structure. The growth of the effective free-energy barriers with increasing density is consistent with the Vogel-Fulcher law, and this growth is primarily driven by an entropic mechanism.