  We investigate the parameter space of hybrid inflation models where inflation
terminates via a first-order phase transition causing nucleation of bubbles.
Such models experience a tension from the need to ensure nearly scale invariant
density perturbations, while avoiding a near scale-invariant bubble size
distribution which would conflict observations. We perform an exact analysis of
the different regimes of the models, where the energy density of the inflaton
field ranges from being negligible as compared to the vacuum energy to
providing most of the energy for inflation. Despite recent microwave anisotropy
results favouring a spectral index less than one, we find that there are still
viable models that end with bubble production and can match all available
observations. As a by-product of our analysis, we also provide an up-to-date
assessment of the viable parameter space of Linde's original second-order
hybrid model across its full parameter range.
