1. This paper reviews methods used to estimate bird population index numbers and proposes a new method. 2. An index number for a year is defined as the ratio of the population size in the year to the population size in the base year. In the context of waterbird populations, the major problem with generating index numbers is the fact that, owing to missing observations at a subset of localities, the total population size in any year is unknown. 3. We suggest a model-based approach to imputing missing observations so that the total population size at the localities may be estimated and used to produce a series of index numbers of the population sizes each year. The proposed model is multiplicative, with each observation being modelled as the product of three factors: a year factor (the `index number'), a site factor and a month factor. The model assumes that the three factors are independent. 4. Bootstrap methods which enable approximate consistency intervals (analogous to confidence intervals) for the index numbers are devised. 5. The methodology is illustrated by application to winter surveys conducted by the Birds of Estuaries Enquiry (BoEE) of the British Trust for Ornithology. The BoEE data set for grey plover Pluvialis squatarola L. was chosen to illustrate the methods. 6. The results show that index numbers based on a single count per year cannot be considered as representative of the winter as a whole. More reliable index numbers are obtained by basing them on more than one count a year. In the BoEE context, this means using an appropriate group of months. Because fewer BoEE surveys are conducted at the beginning and end of winter, a balance has to be struck between index numbers that integrate bird numbers over an extended period and imputing a large proportion of missing observations. 7. By-products of the proposed methodology are site factors and month factors, which can be used, respectively, to produce objective and politically defensible estimates of the relative importance of an estuary over extended periods, and to discuss migration phenology. The month factors may also prove useful in selecting the group of months upon which to base a series of index numbers. 8. The results suggest that the assumption of independence made in the model is tenable. Departures from this assumption can be examined by analysing patterns in the residuals. 9. Even though missing observations can be imputed, every attempt should continue to be made to encourage observers to complete surveys on as many of the BoEE monthly count dates as possible. The motivation for doing so is strengthened by the knowledge that all winter surveys, not only the January survey, can be used in computing the annual index numbers.