  We describe a scheme for the exploration of quantum gravity phenomenology
focussing on effects that could be thought as arising from a fundamental
granularity of space-time. In contrast with the simplest assumptions, such
granularity is assumed to respect Lorentz Invariance but is otherwise left
unspecified. The proposal is fully observer covariant, it involves non-trivial
couplings of curvature to matter fields and leads to a well defined
phenomenology. We present the effective Hamiltonian which could be used to
analyze concrete experimental situations, some of which are briefly described,
and we shortly discuss the degree to which the present proposal is in line with
the fundamental ideas behind the equivalence principle.
