The brain estimates visual motion by decoding the responses of populations of neurons. Extracting unbiased motion estimates from early visual cortical neurons is challenging because each neuron contributes an ambiguous (local) representation of the visual environment and inherently variable neural response. To mitigate these sources of noise, the brain can pool across large populations of neurons, pool each neuron’s response over time, or a combination of the two. Recent psychophysical and physiological work points to a flexible motion pooling system which arrives at different computational solutions over time and for different stimuli. Here we ask whether a single, likelihood-based computation can accommodate the flexible nature of spatiotemporal motion pooling in humans. We examined the contribution of different computations to human observers’ performance on two global visual motion discriminations tasks, one requiring the combination of motion directions over time, another requiring their combination in different relative proportions over space and time. Observers’ perceived direction of global motion was accurately predicted by a vector average read-out of direction signals accumulated over time and a maximum likelihood read-out of direction signals combined over space, consistent with the notion of a flexible motion pooling system that uses different computations over space and time. Further simulations of observers’ performance with a population decoding model revealed a more parsimonious solution: flexible spatiotemporal pooling could be accommodated by a single computation that optimally pools motion signals across a population of neurons which accumulate local motion signals on their receptive fields at a fixed rate over time.