  We show how to evaluate one-dimensional Minkowski-region Mellin-Barnes
representations arising from massive loop integrals, by modifying the contours
of integration. We implement an exact solution to the differential equation
determining the contours of stationary phase. We also present several simple
approximations to these contours. Our approach points the way to more efficient
computations of massless and massive Mellin-Barnes integrals in both Euclidean
and Minkowski regions.
