Birds flying through a cluttered environment require the ability to choose routes that will take them through the environment safely and quickly. We have investigated some of the strategies by which they achieve this. We trained budgerigars to fly through a tunnel in which they encountered a barrier that offered two passages, positioned side by side, at the halfway point. When one of the passages was substantially wider than the other, the birds tended to fly through the wider passage to continue their transit to the end of the tunnel, regardless of whether this passage was on the right or the left. Evidently, the birds were selecting the safest and quickest route. However, when the two passages were of equal or nearly equal width, some individuals consistently preferred the left-hand passage, while others consistently preferred the passage on the right. Thus, the birds displayed idiosyncratic biases when choosing between alternative routes. Surprisingly--and unlike most of the instances in which behavioral lateralization has previously been discovered--the bias was found to vary from individual to individual, in its direction as well as its magnitude. This is very different from handedness in humans, where the majority of humans are right-handed, giving rise to a so-called population bias. Our experimental results and mathematical model of this behavior suggest that individually varying lateralization, working in concert with a tendency to choose the wider aperture, can expedite the passage of a flock of birds through a cluttered environment.