  We have modelled the evolution of cometary HII regions produced by zero-age
main-sequence stars of O and B spectral types, which are driving strong winds
and are born off-centre from spherically symmetric cores with power-law
($\alpha = 2$) density slopes. A model parameter grid was produced that spans
stellar mass, age and core density. Exploring this parameter space we
investigated limb-brightening, a feature commonly seen in cometary HII regions.
We found that stars with mass $M_\star \geq 12\, \mathrm{M}_\odot$ produce this
feature. Our models have a cavity bounded by a contact discontinuity separating
hot shocked wind and ionised ambient gas that is similar in size to the
surrounding HII region. Due to early pressure confinement we did not see shocks
outside of the contact discontinuity for stars with $M_\star \leq 40\,
\mathrm{M}_\odot$, but the cavities were found to continue to grow. The cavity
size in each model plateaus as the HII region stagnates. The spectral energy
distributions of our models are similar to those from identical stars evolving
in uniform density fields. The turn-over frequency is slightly lower in our
power-law models due to a higher proportion of low density gas covered by the
HII regions.
