We examine the relationship between environment and the luminosities,surface brightnesses, colors, and profile shapes of luminous galaxies inthe Sloan Digital Sky Survey (SDSS). For the SDSS sample, galaxy coloris the galaxy property most predictive of the local environment. Galaxycolor and luminosity-measures of the star formation history-jointlycomprise the most predictive pair of properties. At fixed luminosity andcolor, density is not closely related to surface brightness or toSérsic index-measures of galaxy structure. In the text, wediscuss what measurable residual relationships exist, generally findingthat at red colors and fixed luminosity, the mean density decreases atthe highest surface brightnesses and Sérsic indices. In general,these results suggest that the structural properties of galaxies areless closely related to galaxy environment than are their masses andstar formation histories.Based on observations obtained with the Sloan Digital Sky Survey.