The number of HIV-infected people is an important measure of the magnitude of the AIDS epidemic in Brazil and allows for comparison with epidemic patterns in other countries. This quantity can be estimated from the number of reported AIDS cases, which in turn needs to be corrected for the distribution of reporting delays and under-recording of cases. These distributions are unknown and must also be estimated from the recorded dates, which were missed to the Brazilian National AIDS registry. This paper estimates the number of AIDS cases diagnosed by imputing the lost information based on an estimate of the pattern in registration delay until 1996. We first fitted a non-stationary bivariate Poisson regression model to estimate the pattern in reporting delay. In the subsequent steps these models were applied to impute new data, thus replacing the missing information, and to estimate the magnitude of the AIDS epidemic in the country. Model estimates ranged from 36,000 to 50,000 AIDS cases diagnosed in Brazil and still unreported. Therefore, the epidemic was 20 to 30% greater than known from the available information as of February 1999. To be useful to health policy-makers, the surveillance system based on officially reported AIDS cases must be continuously improved.