  The observational indications for a constant specific star-formation rate
(sSFR) in the redshift range z=2-7 are puzzling in the context of current
galaxy-formation models. Despite the tentative nature of the data, their marked
conflict with theory motivates a study of the possible implications. The
plateau at sSFR ~ 2 Gyr^-1 is hard to reproduce because (a) its level is low
compared to the cosmological specific accretion rate at z > 6, (b) it is higher
than the latter at z ~ 2, (c) the natural correlation between SFR and stellar
mass makes it difficult to manipulate their ratio, and (d) a low SFR at high z
makes it hard to produce enough massive galaxies by z ~ 2. Using a flexible
semi-analytic model, we explore ad-hoc modifications to the standard physical
recipes trying to obey the puzzling observational constraints. Successful
models involve non-trivial modifications, such as (a) a suppressed SFR at z > 4
in galaxies of all masses, by enhanced feedback or reduced SFR efficiency,
following an initial active phase at z > 7, (b) a delayed gas consumption into
stars, allowing the gas that was prohibited from forming stars or ejected at
high z to form stars later in more massive galaxies, and (c) enhanced growth of
massive galaxies, in terms of either faster assembly or more efficient
starbursts in mergers, or by efficient star formation in massive haloes.
