In recent years, different alternatives have been suggested to specify and estimate gravity models for bilateral trade. Presently, the so-called Poisson pseudomaximum likelihood (PPML) with log-linear index is probably the most commonly used method. A method is proposed for panel data that targets to reconcile the pros and cons of fixed and random effects models, respectively. It applies equally to two- and three-way panel models and those with country-specific time-varying effects. It allows to filter out potential correlation between observed and unobserved heterogeneity and to identify the effects of time-invariant factors. It can also be used when panels are short in time, and to other specifications than the PPML-like gamma PML, zero-inflated, or Tobit-like models. We introduce and illustrate the proposed estimator with a study of bilateral trade flows across the European Union before the recent economic crisis.