  There have been several recent detections of candidate Keplerian discs around
massive young protostars. Given the relatively large disc-to-star mass ratios
in these systems, and their young ages, it is worth investigating their
propensity to becoming self-gravitating. To this end, we compute
self-consistent, semi-analytic models of putative self-gravitating discs for
five candidate disc systems. Our aim is not to fit exactly the observations,
but to demonstrate that the expected dust continuum emission from marginally
unstable self-gravitating discs can be quite weak, due to high optical depth at
the midplane even at millimetre wavelengths. In the best cases, the models
produce "observable" disc masses within a factor of <1.5 of those observed,
with midplane dust temperatures comparable to measured temperatures from
molecular line emission. We find in two cases that a self-gravitating disc
model compares well with observations. If these discs are self-gravitating,
they satisfy the conditions for disc fragmentation in their outer regions.
These systems may hence have as-yet-unresolved low mass stellar companions, and
are thus promising targets for future high angular resolution observations.
