We measure the sizes for a sample of 174 Lyα-selected galaxies with broadband imaging with the Hubble Space Telescope. Over the redshift range 2.25 < z < 6, Lyα-selected galaxies have a characteristic, constant, small size in rest-frame ultraviolet (UV) light. Coupled with a characteristic star formation intensity (i.e., UV luminosity per unit area), this can explain their non-evolving ultraviolet continuum luminosity function. This is in contrast to Lyman break galaxies (LBGs) over the same redshift range, which have been previously shown to increase in linear size as H(z)–1. The compact physical size seems to be a critical determining factor in whether a galaxy will show Lyα emission or not. The L * of LBGs and its evolution with redshift can be derived from a simple model where the star formation intensity has an upper limit set by feedback processes, independent of redshift. The increase in L * of LBGs is mainly driven by the increase in linear size over redshifts for z = 2-7. Since Lyα galaxies do not grow in linear size, they do not show an increase in L *.