The high-resolution Miniball germanium detector array has been operational at REX-ISOLDE at CERN for over 10 years. This array consists of 24 six-fold segmented, tapered, encapsulated high-purity germanium crystals and was specially designed for low multiplicity experiments with low-intensity radioactive ion beams (RIB). For work with rare-isotope beams, the multiplicities are low (often only a few states are excited) and the yields of such beams are usually much lower than for conventional experiments, so efficiency is paramount. High granularity and high efficiency were achieved by the segmentation of the charge-collection electrodes of the Ge detectors and the use of pulse-shape analysis to determine the position of the first interaction of the γ ray within the Ge crystal, giving a spatial resolution significantly finer than the dimensions of the crystal. The Miniball array has been used in numerous Coulomb-excitation and transfer-reaction experiments with exotic RIBs with energies up to 3 MeV/u, produced at the ISOLDE facility.