  We refine a technique to measure the absorption corrected ultraviolet (UV)
luminosity of starburst galaxies using rest frame UV quantities alone, and
apply it to U-dropouts at z ~ 3 found in the Hubble Deep Field. The method is
based on an observed correlation between the ratio of far infrared (FIR) to UV
fluxes with spectral slope \beta (a UV color). A simple fit to this relation
allows the UV flux absorbed by dust to be calculated, and hence the dust-free
UV luminosity to be determined. IUE spectra and IRAS fluxes of local starbursts
are used to calibrate the ratio in terms of 1600 Angstrom absorption A_{1600},
and the transformation from broad band color to \beta. We show that the recent
marginal and non-detections of HDF U-dropouts in the radio and sub-mm are
consistent with our calculated A_{1600}. This is also true of observations of
the ratio of optical emission line flux to UV flux density in the brightest
U-dropouts. This latter ratio turns out not to be a good indicator of dust
extinction. In U-dropouts, absolute magnitude correlates with \beta: brighter
galaxies are redder, as is observed in local starburst galaxies. This suggests
that a mass-metallicity relationship is in place by z ~ 3. The UV luminosity
function of U-dropouts extends up to M_{1600,0} ~ -24 ABmag corresponding to a
star formation rate ~ 200 \Msun/yr (H_0 = 50 km/s/Mpc, q_0 = 0.5). The
absorption-corrected UV luminosity density at z ~ 3 is \rho_{1600,0} =>
1.4x10^{27} erg/s/Hz/Mpc^3; still a lower limit since completeness corrections
have not been done and because only galaxies with A_{1600} < ~3.6 mag are blue
enough to be selected as U-dropouts. The luminosity weighted mean dust
absorption factor of our sample is 5.4 +/- 0.9$ at 1600\AA (abridged).
