  There is growing evidence that, at the S(850) < 1 mJy level, the sub-mm
galaxy population (and hence a potentially significant fraction of the sub-mm
background) is associated with the star-forming Lyman-break population already
detected at optical wavelengths. However, the implied star-formation rates in
such objects (typically 3-30 solar masses per year) fall one or two orders of
magnitude short of the level of star-forming activity required to produce the
most massive elliptical galaxies on a timescale ~ 1 Gyr. If a significant
fraction of massive ellipticals did form the bulk of their stars in short-lived
massive starbursts at high redshift, then they should presumably be found among
the brighter, S(850) ~ 10 mJy sub-mm sources which are undoubtedly not part of
the Lyman-break population. A first powerful clue that this is indeed the case
comes from our major SCUBA survey of radio galaxies, which indicates that
massive dust-enshrouded star-formation in at least this subset of massive
ellipticals is largely confined to z > 2.5, with a mean redshift z = 3.5. While
radio selection raises concerns about bias, I argue that our current knowledge
of the brightest (S(850) ~ 10 mJy) sub-mm sources detected in unbiased SCUBA
imaging surveys indicates that they are also largely confined to this same
high-z regime. Consequently, while the most recent number counts imply such
extreme sources can contribute only 5-10% of the sub-mm background, their
comoving number density (in the redshift band 3 < z < 5) is 1-2 x 10^{-5} per
cubic megaparsec, sufficient to account for the formation of all ellipticals of
comparable mass to radio galaxies (~4L-star) in the present-day universe.
