We measured the transmission of tapered and untapered optical fibres as a function of input beam numerical aperture at 635 nm. The tapered fibres were fabricated with an adiabatic tapering process from graded and step-index fibres with 50 m core diameters to form a 100 mm long taper with 5:1 taper ratio. We tested tapered graded-index and step-index fibres fabricated from commercial Thorlabs products and a custom graded-index taper. The 5:1 tapered graded-index fibre can give a transmission greater than 0.4 for Thorlabs and 0.6 for the custom taper. We simulated the transmission of the tapered fibres and found reasonable agreement with the measured graded-index tapered fibre results across the numerical aperture range of interest. Experimentally, step-index tapered fibres performed relative poorly and considerably below modelling expectations. Based on our examinations this arises because the properties of step-index fibre were not robust to the tapering process. Suitably tapered graded-index fibres may offer a new route for efficient focal ratio reduction of fibre optic signals, e.g., in fibre-fed spectrographs, though we stress that our measurements have been limited to monochromatic light in this work.