The incubation period, the time between infection and disease onset, is important in the surveillance and control of infectious diseases but is often coarsely observed. Coarse data arises because the time of infection, the time of disease onset or both are not known precisely. Accurate estimates of an incubation period distribution are useful in real-time outbreak investigations and in modeling public health interventions. We compare two methods of estimating such distributions. The first method represents the data as doubly interval-censored. The second introduces a data reduction technique that makes the computation more tractable. In a simulation study, the methods perform similarly when estimating the median, but the first method yields more reliable estimates of the distributional tails. We conduct a sensitivity analysis of the two methods to violations of model assumption and we apply these methods to historical incubation period data on influenza A and respiratory syncytial virus. The analysis of reduced data is less computationally intensive and performs well for estimating the median under a wide range of conditions. However for estimation of the tails of the distribution, the doubly interval-censored analysis is the recommended procedure.