  We explore the possibility of using UV spectroscopy in combination with
broad-band photometry as diagnostic tools for understanding the shape of the
Initial Mass Function (IMF) in unresolved stellar populations. Building on our
previous work, we extend the Stochastically Lighting Up Galaxies code (slug) to
include a high-resolution UV spectral synthesiser and equivalent width
calculation capabilities. We first gain a qualitative understanding of how UV
spectral features behave as the parameters that define a star cluster in slug
(mass, age, extinction, and IMF slope alpha) are changed. We then exploit
Bayesian inference techniques to recover the alpha values for clusters
simulated with slug, using mock observations of these clusters comprised of
broad-band photometry and equivalent width measurements of a selection of UV
spectral features. We find some improvement when compared to attempts using
broad-band photometry alone (with the interquartile range of the alpha
posterior PDF shrinking by 32%), although we still do not yet fully break the
known degeneracy between the cluster mass and alpha. Finally, we make
predictions about how effective real observations will be by quantifying our
ability to constrain alpha as a function of limiting equivalent width. We find
that observations sensitive to a modest equivalent width of 9 A are sufficient
to improve the recovery of the IMF slope parameter by 32% (interquartile range
of posterior PDF median residuals), moving to 39% when we include all the
significant spectral features in the wavelength range 900-3000 A.
