In nonlinear panel data models, the incidental parameter problem remains a challenge to econometricians. Available solutions are often based on ingenious, model-specific methods. In this paper, we propose a systematic approach to construct moment restrictions on common parameters that are free from the individual fixed effects. This is done by an orthogonal projection that differences out the unknown distribution function of individual effects. Our method applies generally in likelihood models with continuous dependent variables where a condition of non-surjectivity holds. The resulting method-of-moments estimators are root-N consistent (for fixed T) and asymptotically normal, under regularity conditions that we spell out. Several examples and a small-scale simulation exercise complete the paper.