  Differential Privacy (DP) provides tight upper bounds on the capabilities of
optimal adversaries, but such adversaries are rarely encountered in practice.
Under the hypothesis testing/membership inference interpretation of DP, we
examine the Gaussian mechanism and relax the usual assumption of a
Neyman-Pearson-Optimal (NPO) adversary to a Generalized Likelihood Test (GLRT)
adversary. This mild relaxation leads to improved privacy guarantees, which we
express in the spirit of Gaussian DP and $(\varepsilon, \delta)$-DP, including
composition and sub-sampling results. We evaluate our results numerically and
find them to match the theoretical upper bounds.
