One major difficulty in probing the nature of Lyman break galaxies (LBGs) at z ˜ 3 is the mismatch between our best images of LBGs, which are in the rest-UV, and the best images of local galaxies, which are in the rest-optical. To make direct comparisons between LBGs at z ˜ 3 and more local star-forming galaxies, we use HST/STIS to image a set of 12 nearby (z<0.05) H II galaxies in the FUV and a set of 14 luminous blue compact galaxies (LBCGs) at moderate redshift (z ˜ 0.5) in the NUV, corresponding to the rest-FUV. We then subject both sets of galaxy images to the same morphological measurements recently applied to LBGs at z ˜ 3 in the Hubble Deep Field-North. We find many qualitative and quantitative similarities between the rest-FUV characteristics of distant LBGs and of the more nearby starburst samples, including sizes, asymmetries, and concentrations. This implies that, like the nearby H II galaxies and LBCGs, LBGs may be predominately low-mass, extreme starbursts, with a high merger fraction.