  We present models for dusty high-redshift Lyman alpha emitting galaxies by
combining the Press-Schechter formalism with a treatment of inhomogeneous dust
distribution inside galaxies. These models reproduce the surface density of
emitters inferred from recent observations, and also agree with previous
non-detections. Although a detailed determination of the individual model
parameters is precluded by uncertainties, we find that (i) the dust content of
primordial galaxies builds up in no more than 5x10^8 years, (ii) the galactic
HII regions are inhomogeneous with a cloud covering factor of order unity, and
(iii) the overall star formation efficiency is at least 5 percent. Future
observations should be able to detect Lyman alpha galaxies upto redshifts of
about z=8. If the universe is reionized at z(reion)<8, the corresponding
decline in the number of Lyman alpha emitters at z>z(reion) could prove to be a
useful probe of the reionization epoch.
