  Using a novel and self-consistent approach that avoids the scalar-tensor
identification in the Einstein frame, we reanalyze the viability of f(R)
gravity within the context of solar-system tests. In order to do so, we depart
from a simple but fully relativistic system of differential equations that
describe a compact object in a static and spherically symmetric spacetime, and
then we make suitable linearizations that apply to nonrelativistic objects such
as the Sun. We then show clearly under which conditions the emerging
chameleonlike mechanism can lead to a post-Newtonian parameter {\gamma}
compatible with the observational bounds. To illustrate this method, we use
several specific f(R) models proposed to explain the current acceleration of
the Universe, and we show which of them are able to satisfy those bounds.
