  The STE-QUEST space mission will perform tests of the gravitational redshift
in the field of the Sun and the Moon to high precision by frequency comparisons
of clocks attached to the ground and separated by intercontinental distances.
In the absence of Einstein equivalence principle (EP) violation, the redshift
is zero up to small tidal corrections as the Earth is freely falling in the
field of the Sun and Moon. Such tests are thus null tests, allowing to bound
possible violations of the EP. Here we analyze the Sun/Moon redshift tests
using a generic EP violating theoretical framework, with clocks minimally
modelled as two-level atoms. We present a complete derivation of the redshift
(including both GR and non-GR terms) in a realistic experiment such as the one
envisaged for STE-QUEST. We point out and correct an error in previous
formalisms linked to the atom's recoil not being properly taken into account.
