Francis Hauksbee (1660–1713) is well known for his double-barrelled air-pump. However, the origin of this pump, and Hauksbee's background, are often described as a mystery. This text seeks to dispel the riddle. It is argued that Hauksbee's competence as an exceptional maker of air-pumps was developed between 1699 and 1703 as a result of his experiences with the construction, manufacturing and sale of cupping-glasses. His cupping utensils embodied a new design, where syringes were used to evacuate the glasses, instead of the traditional way by fire or mouth suction. These syringes, which in fact were small air-pumps, were perfected between 1699 and 1701. A larger syringe, introduced in 1701, served as a transition from the cupping-syringe to his first air-pump for use in natural philosophy. This syringe was described as a ‘combined engine’, which could serve as an air-pump, a condensing engine and a syringe for injecting air, wax or mercury into pathological specimens. Hauksbee's first air-pump was a single-barrelled model introduced in 1702, based on the combined engine. Its various features, such as easy and convenient leak-tightening, exact pressure measurements by an in-built barometer and an air-inlet function for readmission of air into the receiver, are discussed. Finally, it is shown that these activities gave Hauksbee the reputation of being an outstanding instrument-maker, years before the double-barrelled air-pump was in sight.