While efficient fibre-waveguide coupling has been achieved for titanium-diffused waveguides on Z-cut Y-propagating lithium niobate crystals, previously reported results for coupling to waveguides on non-Z-cut crystals have been poor. Here we report total fibre-waveguide-fibre insertion losses as low as −1.35 dB for ∼l.5 cm-long waveguides on X-cut Y-propagating lithium niobate—the preferable orientation for polarisation conversion devices. The losses are only slightly higher than the best value for Z-cut crystals (∼ −1 dB) due to the larger waveguide mode eccentricity. While efficient fibre-waveguide coupling has been achieved for titanium-diffused waveguides on Z-cut Y-propagating lithium niobate crystals, previously reported results for coupling to waveguides on non-Z-cut crystals have been poor. Here we report total fibre-waveguide-fibre insertion losses as low as −1.35 dB for ∼l.5 cm-long waveguides on X-cut Y-propagating lithium niobate—the preferable orientation for polarisation conversion devices. The losses are only slightly higher than the best value for Z-cut crystals (∼ −1 dB) due to the larger waveguide mode eccentricity.