The core-cladding composition difference is a crucial element in the design of high numerical apertures for single-mode fluoride glass optical fibres. The larger the numerical aperture, the more light that can be launched into the fibre core. Starting with well known stable glass compositions containing zirconium fluoride, PbF2, LiF and GaF3 have been introduced into the core and cladding respectively to increase the difference in refractive index, Δn, and thus increase the numerical aperture, while still maintaining a high degree of stability. A refractive index difference, Δn, of 0.06 and numerical aperture of 0.41 was obtained for compositions (ZrF4-BaF2-LaF3-AlF3-LiF-PbF2 (ZBLALiPb3) for the core and ZrF4-BaF2-LaF3-AlF3-NaF-GaF3 (ZBLNGa13) for the cladding), where the difference in the glass transition temperature, Tg, was only 4°C. The relationship between the differences in refractive index, Δn, and glass transition temperature, ΔTg, with compositional changes of the glass host are discussed.