By inverting the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) hard X-ray photon spectrum with the Tikhonov regularization algorithm, we infer the effective mean electron source spectrum for a time interval near the peak of the 2002 July 23 event. This inverse approach yields the smoothest electron flux spectrum consistent with the data while retaining real features, such as local minima, that cannot be found with forward model-fitting methods that involve only a few parameters. A significant dip in the recovered mean source electron spectrum near E = 55 keV is noted, and its significance briefly discussed.