  Observations in the submillimetre waveband have recently revealed a new
population of luminous, sub-mm sources. These are proposed to lie at high
redshift and to be optically faint due to their high intrinsic dust
obscuration. The presence of dust has been previously invoked in optical galaxy
count models which assume $\tau=9$ Gyr Bruzual & Charlot evolution for spirals
and these fit the count data well from U to K. We now show that by using either
a 1/$\lambda$ or Calzetti absorption law for the dust and re-distributing the
evolved spiral galaxy UV radiation into the far infra-red(FIR), these models
can account for all of the `faint'($\leq1$mJy) $850\mu$m galaxy counts, but
fail to fit 'bright'($\ge2$mJy) sources, indicating that another explanation
for the sub-mm counts may apply at brighter fluxes(e.g. QSOs, ULIRGs). We find
that the main contribution to the faint, sub-mm number counts is in the
redshift range $0.5 < z < 3$, peaking at $z\approx 1.8$. The above model, using
either dust law, can also explain a significant proportion of the
extra-galactic background at $850\mu$m as well as producing a reasonable fit to
the bright $60\mu m$ IRAS counts.
