Using semi-analytic models of galaxy formation set within the cold dark mat
ter (CDM) merging hierarchy, we investigate several scenarios for the natur
e of the high-redshift (z greater than or similar to 2) Lyman-break galaxie
s (LBGs). We consider a 'collisional starburst' model in which bursts of st
ar formation are triggered by galaxy-galaxy mergers, and find that a signif
icant fraction of LBGs are predicted to be starbursts. This model reproduce
s the observed comoving number density of bright LBGs as a function of reds
hift and the observed luminosity function at, z similar to 3 and z similar
to 4, with a reasonable amount of dust extinction. Model galaxies at z simi
lar to 3 have star formation rates, half-light radii, I - K colours and int
ernal velocity dispersions that are in good agreement with the data. Global
quantities such as the star formation rate density and cold gas and metal
content of the Universe as a function of redshift also agree well. Two 'qui
escent' models without starbursts are also investigated. In one, the star f
ormation efficiency in galaxies remains constant with redshift, while in th
e other, it scales inversely with disc dynamical time, and thus increases r
apidly with redshift. The first quiescent model is strongly ruled out, as i
t does not produce enough high-redshift galaxies once realistic dust extinc
tion is accounted for. The second quiescent model fits marginally, but unde
rproduces cold gas and very bright galaxies at high redshift. A general con
clusion is that star formation at high redshift must be more efficient than
locally. The collisional starburst model appears to accomplish this natura
lly without violating other observational constraints.