High-resolution UCLES/AAT spectra are presented for nine B-type supergiants in the SMC, chosen on the basis that they may show varying amounts of nuclear-synthetically processed material mixed to their surface. These spectra have been analysed using a new grid of approximately 12 000 non-LTE line blanketed tlusty model atmospheres to estimate atmospheric parameters and chemical composition. The abundance estimates for O, Mg and Si are in excellent agreement with those deduced from other studies, whilst the low estimate for C may reflect the use of the C II doublet at 4267 Å. The N estimates are approximately an order of magnitude greater than those found in unevolved B-type stars or H II regions but are consistent with the other estimates in AB-type supergiants. These results have been combined with results from a unified model atmosphere analysis of UVES/VLT spectra of B-type supergiants (Trundle et al. 2004, A&A, 417, 217) to discuss the evolutionary status of these objects. For two stars that are in common with those discussed by Trundle et al., we have undertaken a careful comparison in order to try to understand the relative importance of the different uncertainties present in such analyses, including observational errors and the use of static or unified models. We find that even for these relatively luminous supergiants, tlusty models yield atmospheric parameters and chemical compositions similar to those deduced from the unified code fastwind.