Abstract Three-dimensional variational data assimilation (3D-Var) with the first guess at appropriate time (FGAT) appears to be an attractive compromise between accuracy and overall computing time. It is computationally cheaper than four-dimensional (4D)-Var as the increment is not propagated back and forth in time by a model, yet the comparison between the model and the observations is still computed at the right observation time. An interesting feature of the 4D-Var is the iterative process known as the outer loop. This outer-loop approach can also be used in conjunction with 3D-FGAT. But it requires the application of the 3D-FGAT analysis increment at the beginning of the assimilation window. The pros and cons of using this unusual 3D-FGAT variant are illustrated in this paper on two applications focused on the transport, one of the main phenomena governing the atmospheric evolution. The first one is the one-dimensional advection of a passive tracer. By three representative situations, it shows the benefits of the outer loop, except for practical situations driven by very rapid dynamics such as a zonal wind of 50 m s−1 on the earth’s great circle, when the assimilation window has a size of 3 h. The second application is the 3D-FGAT assimilation of true ozone measurements into a chemical–transport model. It confirms the previous results, showing that the 3D-FGAT analysis with the outer loop produces an overestimation of the ozone increment in regions where the wind speed is high compared to the time length of the assimilation window.