We report on video-microscopy measurements of the translational and rotational Brownian motions of isolated ellipsoidal particles in quasi-two-dimensional sample cells of increasing thickness. The long-time diffusion coefficients were measured along the long (Da) and short (Db) ellipsoid axes, respectively, and the ratio, Da /Db, was determined as a function of wall confinement and particle aspect ratio. In three dimensions (3D), this ratio (Da /Db) cannot be larger than 2, but in quasi-two dimensions, wall confinement was found to substantially alter diffusion anisotropy and substantially slow particle diffusion along the short axis compared to 3D.