IF the current abundance of interplanetary dust is representative of its long-term value1, there must be a source of dust replenishing the ∼107 g s–1 (mostly in the form of particles of 10–4 to 1 g) destroyed by dissipative processes2. Short-period comets are the most likely such source3, but their dust production rate is uncertain. Coma spectrophotometry of several short-period comets excludes significant contributions of dust from them4,5, but observations by the Infrared Astronomical Satellite6 have suggested the opposite. Here I use a numerical model7 to analyse an optical image of the dust tail of comet P/Schwassman–Wachmann 1, which contains information about grains 5 μm to 2 cm in diameter, ejected from 900 to 30 days before perihelion. During the three years covered by the model, the mass loss rate reached an estimated (6±3) × 105 g s–1, for an assumed albedo9 of 0.1 at the observation phase angle of 4°. This one short-period comet thus apparently provides ∼6% of the mass required to balance the losses of the interplanetary dust cloud.