  We show that Solar System tests can place very strong constraints on
K-mouflage models of gravity, which are coupled scalar field models with
nontrivial kinetic terms that screen the fifth force in regions of large
gravitational acceleration. In particular, the bounds on the anomalous
perihelion of the Moon imposes stringent restrictions on the K-mouflage
Lagrangian density, which can be met when the contributions of higher-order
operators in the static regime are sufficiently small. The bound on the rate of
change of the gravitational strength in the Solar System constrains the
coupling strength $\beta$ to be smaller than $0.1$. These two bounds impose
tighter constraints than the results from the Cassini satellite and Big Bang
Nucleosynthesis. Despite the Solar System restrictions, we show that it is
possible to construct viable models with interesting cosmological predictions.
In particular, relative to $\Lambda$-CDM, such models predict percent-level
deviations for the clustering of matter and the number density of dark matter
haloes. This makes these models predictive and testable by forthcoming
observational missions.
