In Drosophila, most individual olfactory receptor neurons (ORNs) project bilaterally to both sides of the brain. Having bilateral rather than unilateral projections may represent a useful redundancy. However, bilateral ORN projections to the brain should also compromise the ability to lateralize odours. Nevertheless, walking or flying Drosophila reportedly turn towards the antenna that is more strongly stimulated by odour. Here we show that each ORN spike releases approximately 40% more neurotransmitter from the axon branch ipsilateral to the soma than from the contralateral branch. As a result, when an odour activates the antennae asymmetrically, ipsilateral central neurons begin to spike a few milliseconds before contralateral neurons, and at a 30 to 50% higher rate than contralateral neurons. We show that a walking fly can detect a 5% asymmetry in total ORN input to its left and right antennal lobes, and can turn towards the odour in less time than it requires the fly to complete a stride. These results demonstrate that neurotransmitter release properties can be tuned independently at output synapses formed by a single axon onto two target cells with identical functions and morphologies. Our data also show that small differences in spike timing and spike rate can produce reliable differences in olfactory behaviour.