This is part of a bird oriented series that concentrates on species that occur in the central part of the state at least for part of the year (primarily during nesting season).
The Eastern Phoebe (Sayornis phoebe) is a flycatcher that will utilize a nest shelf in buildings or under bridges. It is known to nest in Arkansas and perhaps can be found nesting in Louisiana (at least in the NW part). It is a common winter resident. The best field mark is the figure-8 tail wagging and its dark head.
Other birds that will utilize a nest shelf are American Robin and Barn Swallow.