The use of two-way fixed-effect models is widespread. The presence of incidental parameter bias, however, invalidates statistical inference based on the likelihood. In this paper we consider modifications to the (profile) likelihood that yield asymptotically unbiased estimators as well as likelihood-ratio and score tests with correct size. The modifications are widely applicable and easy to implement. Our examples illustrate that the modifications can lead to dramatic improvements relative to the maximum likelihood method both in terms of point estimation and inference.