The controlled delivery of fluids is a key process in nature and in many areas of science and technology, where pipettes or related devices are used for dispensing well-defined fluid volumes. Existing pipettes are capable of delivering fluids with attolitre (10(-18) l) accuracy at best(1). Studies on phase transformations of nanoscale objects would benefit from the controlled dispensing and manipulation of much smaller droplets. In contrast to nanoparticle melting whose fundamental pathway was studied extensively(2), experiments on crystallization, testing classical nucleation theory(3), are hindered by the influence of support interfaces. Experiments on free-standing fluid drops are extremely challenging(4). Here, we demonstrate the operation of a pipette, which, observed by transmission electron microscopy, delivers a metal-alloy melt with zeptolitre (10(-21) l) resolution. We use this exquisite control to produce nearly free-standing Au72Ge28 drops suspended by an atomic-scale meniscus at the pipette tip, and to image their phase transformations with near-atomic resolution. Our observations of the liquid-solid transition challenge classical nucleation theory3 by providing experimental evidence for an intrinsic crystallization pathway of nanometre-sized fluid drops that avoids nucleation in the interior, but instead proceeds via liquid-state surface faceting as a precursor to surface-induced crystallization.