We examine the hypothesis that wandering albatrosses (Diomedea exulans) undergo Levy flights when roaming the skies in search of oceanic food sources. Levy flights are random walks whose step lengths are taken from a distribution with infinte variance, such as a power-law. The Levy flight consequently has no typical scale, and this has been interpreted as being an efficient way of searching for food on the ocean surface. We first re-analyse the original data that were used to infer Levy flights. These data come from wet/dry loggers that record the time periods for which the birds were airborne or on the ocean surface. We cast doubt as to whether these data are sufficient to conclude Levy flight behaviour. This prompts us to analyse recent data from birds fitted with much higher resolution wet/dry loggers. We find that the widely-held Levy flight hyopthesis can be refuted by the newer data. We will also briefly discuss other data sets and ecological questions arising from the unique Antarctic environment.