  We explore the space of spherically symmetric, static solutions in the
decoupling limit of a class of non-linear covariant extensions of Fierz-Pauli
massive gravity obtained recently in arXiv:1007.0443. In general, several such
solutions with various asymptotic limits exist. We find their approximate short
and long-distance behaviour and use numerical analysis to match them at the
Vainshtein radius, $r_*$. Our findings indicate, that for a broad range of
parameters, the theory does possess the Vainshtein mechanism, screening the
scalar contribution to the gravitational force within $r_*$. In addition, there
exists a class of solutions in the literature, for which the $1/r$
gravitational potential is completely screened within the Vainshtein scale.
However, numerical analysis indicates, that for this type of solutions, the
gravitational potential does not decay at spatial infinity.
