Apparatus for precisely aspirating small volumes of liquid, e.g., a blood sample, contained in a vessel, e.g., a test tube or vial, includes a mechanism for sensing that the tip of an aspirating probe is contacting the bottom of the vessel during the aspiration process. Such a bottom-sensing mechanism is adapted to sense a predetermined forcible interaction between the probe tip and the vessel bottom. In a preferred embodiment, such forcible interaction is sensed by detecting movement of a movably mounted platform that supports the vessel during aspiration. In a second embodiment, the forcible interaction is sensed by detecting the back-emf in a motor winding used to advance the aspiration probe.