The signal-to-noise ratio of a direction-selective neuron for 'detecting' visual motion is highest when the motion direction is close to the neuron's preferred direction. But because these neurons show a bell-shaped tuning for direction, they have the highest signal-to-noise ratio for 'discriminating' the direction of motion when their preferred direction is off the direction to be discriminated. In this paper, we demonstrate with an adaptation paradigm that the visual system shows a corresponding task-specific ability to select neurons depending on whether it is performing a detection or a discrimination task, relying preferentially on different neuronal populations in the two tasks. Detection is based on neuronal populations tuned to the test direction, while direction discrimination is based on neurons preferring directions 40-60 degrees off the test direction.