We present a set of structural parameters for the central parts of 57 early-type galaxies observed with the Planetary Camera of the Hubble Space Telescope. These parameters are based on a new empirical law that successfully characterizes the centers of early type galaxies. This empirical law assumes that the surface brightness profile is a combination of two power laws with different slopes gamma and beta for the inner and outer regions. Conventional structural parameters such as core radius and central surface brightness are replaced by break radius r_b, where the transition between power-law slopes takes place, and surface brightness mu_b at that radius. An additional parameter alpha describes the sharpness of the break. The structural parameters are derived using a chi-squared minimization process applied to the mean surface brightness profiles. The resulting model profiles generally give very good agreement to the observed profiles out to the radius of 10 arcseconds imaged by the Planetary Camera. Exceptions include galaxies which depart from pure power-laws at large radius, those with strong nuclear components, and galaxies partly obscured by dust. The uncertainties in the derived parameters are estimated using Monte-Carlo simulations which test the stability of solutions in the face of photon noise and the effects of the deconvolution process. The covariance of the structural parameters is examined by computing contours of constant chi squared in multi-dimensional parameter space.Comment: 14 pages, 1 table, 8 postscript figures, aaspp4.sty included, accepted for publication in the Astronomical Journa