  We consider the evolution equations for the bulk viscous pressure, diffusion
current and shear tensor derived within second-order relativistic dissipative
hydrodynamics from kinetic theory. By matching the higher order moments
directly to the dissipative quantities, all terms which are of second order in
the Knudsen number Kn vanish, leaving only terms of order
$\mathcal{O}(\textrm{Re}^{-1} \textrm{Kn})$ and $\mathcal{O}(\textrm{Re}^{-2})$
in the relaxation equations, where $\textrm{Re}^{-1}$ is the inverse Reynolds
number. We therefore refer to this scheme as the Inverse-Reynolds-Dominance
(IReD) approach. The remaining (non-vanishing) transport coefficients can be
obtained exclusively in terms of the inverse of the collision matrix. This
procedure fixes unambiguously the relaxation times of the dissipative
quantities, which are no longer related to the eigenvalues of the inverse of
the collision matrix. In particular, we find that the relaxation times
corresponding to higher-order moments grow as their order increases, thereby
contradicting the \textit{separation of scales} paradigm. The formal (up to
second order) equivalence with the standard DNMR approach is proven and the
connection between the IReD transport coefficients and the usual DNMR ones is
established.
