  We compute, using a formula of Dittmann, the Bures metric tensor (g) for the
eight-dimensional convex set of three-level quantum systems, employing a
newly-developed Euler angle-based parameterization of the 3 x 3 density
matrices. Most of the individual metric elements (g_{ij}) are found to be
expressible in relatively compact form, many of them in fact being exactly
zero.
