  Several recent results are reported from work aiming to improve the
quantitative precision of relativistic viscous fluid dynamics for relativistic
heavy-ion collisions. The dense matter created in such collisions expands in a
highly anisotropic manner. Due to viscous effects this also renders the local
momentum distribution anisotropic. Optimized hydrodynamic approaches account
for these anisotropies already at leading order in a gradient expansion.
Recently discovered exact solutions of the relativistic Boltzmann equation in
anisotropically expanding systems provide a powerful testbed for such improved
hydrodynamic approximations. We present the latest status of our quest for a
formulation of relativistic viscous fluid dynamics that is optimized for
applications to relativistic heavy-ion collisions.
