  After a brief review of the first phase of development of Quantum-Gravity
Phenomenology, I argue that this research line is now ready to enter a more
advanced phase: while at first it was legitimate to resort to heuristic
order-of-magnitude estimates, which were sufficient to establish that
sensitivity to Planck-scale effects can be achieved, we should now rely on
detailed analyses of some reference test theories. I illustrate this point in
the specific example of studies of Planck-scale modifications of the
energy/momentum dispersion relation, for which I consider two test theories.
Both the photon-stability analyses and the Crab-nebula synchrotron-radiation
analyses, which had raised high hopes of ``beyond-Plankian'' experimental
bounds, turn out to be rather ineffective in constraining the two test
theories. Examples of analyses which can provide constraints of rather wide
applicability are the so-called ``time-of-flight analyses'', in the context of
observations of gamma-ray bursts, and the analyses of the cosmic-ray spectrum
near the GZK scale.
