  In this paper we present a method for efficiently including the effects of
off-diagonal local rest frame momentum anisotropies in leading-order
anisotropic hydrodynamics. The method relies on diagonalization of the
space-like block of the anisotropy tensor and allows one to reduce the
necessary moments of the distribution function in the off-diagonal case to a
linear combination of diagonal-anisotropy integrals. Once reduced to
diagonal-anisotropy integrals, the results can be computed efficiently using
techniques described previously in the literature. We present a general
framework for how to accomplish this and provide examples for off-diagonal
anisotropy moments entering into the energy-momentum tensor and viscous update
equations which emerge when performing anisotropic pressure matching.
