Producing accurate, reliable indices of abundance, enabling the status of breeding bird populations to be monitored is of interest to government, conservation groups and other bodies. Indices for Sedge Warblers \emph{Acrocephalus schoenobaenus} from 1983 to 2002 were produced using catch data from the British Trust for Ornithology's (BTO) Constant Effort Scheme (CES). This is a ringing programme based on standardised mist-netting across up to 12 annual visits to each of a large number of sites. A feature of these data is that some yearly site counts are ``censored'' due to visits missed within certain years. Peach et al. (1998) developed an intuitive, non-parametric method for correcting for missed visits, prior to model-fitting in the form of a Poisson regression model. In this paper a novel Bayesian approach is introduced, which produces annual indices of abundance whose uncertainty also incorporates a component due to the correction for missed visits. We describe the method in detail, applied to the Sedge Warbler data and to simulated data, and compare the results with those from the current method of Peach et al. (1998).