  We describe a refined version of a previous proposal for the exploration of
quantum gravity phenomenology. Unlike the original scheme, the one presented
here is free from sign ambiguities while it shares with the previous one the
essential features. It focuses on effects that could be thought as arising from
a fundamental granularity of quantum space-time. The sort of schemes we
consider are in sharp contrast with the simplest scenarios in that such
granularity is assumed to respect Lorentz Invariance but it remains otherwise
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, and we shortly review the degree to
which this proposal is in line with the fundamental ideas behind the
equivalence principle.
