  The question of what gravitational theory could supersede General Relativity
has been central in theoretical physics for decades. Many disparate
alternatives have been proposed motivated by cosmology, quantum gravity and
phenomenological angles, and have been subjected to tests derived from
cosmological, solar system and pulsar observations typically restricted to
linearized regimes. Gravitational waves from compact binaries provide new
opportunities to probe these theories in the strongly gravitating/highly
dynamical regimes. To this end however, a reliable understanding of the
dynamics in such a regime is required. Unfortunately, most of these theories
fail to define well posed initial value problems, which prevents at face value
from meeting such challenge. In this work, we introduce a consistent program
able to remedy this situation. This program is inspired in the approach to
"fixing" viscous relativistic hydrodynamics introduced by Israel and Stewart in
the late 70's. We illustrate how to implement this approach to control
undesirable effects of higher order derivatives in gravity theories and argue
how the modified system still captures the true dynamics of the putative
underlying theories in 3+1 dimensions. We sketch the implementation of this
idea in a couple of effective theories of gravity, one in the context of
Non-commutative geometry, and one in the context of Chern-Simons modified
General Relativity.
