In some conservation situations, there is a need for estimates of numbers of seabirds migrating past a specific site, such as sites of proposed offshore wind farms. Migration counts from points strategically located on the coast can be a reliable and effective method of reaching this goal. We propose a consistent and statistically robust method for estimating such numbers by generalized additive modeling of the numbers passing during periods when counts are interrupted. This procedure has the advantage of accounting for the effects of covariates, such as wind, on the counts in a flexible manner, potentially increasing accuracy and precision. We develop a reliable method of estimating precision, based on a parametric bootstrap, and applied a sensitivity analysis to our models to test their accuracy. We demonstrate the method with three species of seabirds migrating through the Strait of Gibraltar. Estimated numbers of the Northern Gannet (Morus bassanus) are similar to the estimated Atlantic population that winters in the western Mediterranean Sea, while for both Cory's (Calonectris diomedea) and Balearic (Puffinus mauretanicus) Shearwaters they are greater than the current population estimates. These results have important implications in conservation and highlight the necessity for reestimation of the latter two species' global population. Potential sources of biases include the constraint on detectability due to distance and the possibility of double counting due to local movements. To avoid overestimates, we suggest that values imputed for the gaps in counts be conservative.