Abstract: The present invention comprises a miniature pump which can be implanted in the eye for controllably removing excess fluid from the eye to treat glaucoma. The pump, in accordance with the inventive method, may be placed beneath the conjunctiva and/or extraocular muscles. In order to ensure that the right amount of fluid is removed from the eye the pump has a variable pumping rate, which results in a variable rate of removal of fluid from the eye. The pumping rate can be manually adjusted or automatically controlled in response to sensed ocular pressure. In the automatic mode, serious complications such as hypotony are avoided by reducing fluid flow when ocular pressure is low.