The classical purpose of optical fibres is delivery of either optical power, as for welding, or temporal information, as for telecommunication. Maximum performance in both cases is provided by the use of single-mode optical fibres. However, transmitting spatial information, which necessitates higher-order modes, is difficult because their dispersion relation leads to dephasing and a deterioration of the intensity distribution with propagation distance. Here we consciously exploit the fundamental cause of the beam deterioration-the dispersion relation of the underlying vectorial electromagnetic modes-by their selective excitation using adaptive optics. This allows us to produce output beams of high modal purity, which are well defined in three dimensions. The output beam distribution is even robust against significant bending of the fibre. The utility of this approach is exemplified by the controlled rotational manipulation of live cells in a dual-beam fibre-optical trap integrated into a modular lab-on-chip system.