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 a 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.