Spallation neutron diffraction and high-energy x-ray diffraction methods have been used to study CaO:Al₂O₃  glasses at the 64:36 mol% eutectic and 50:50 mol% compositions. The samples were produced by the containerless cooling of liquid droplets heated by a laser beam and suspended in an aerodynamic levitator. The results show aluminium on average to be surrounded by 4.0(1) oxygen atoms at a distance of 1.76(1) Å in CaAl₂O₄, which increases to 4.8(1) at the eutectic composition. The two techniques have also been combined to reveal the local structure of the calcium atoms in the glass. In CaAl₂O₄  the calcium is found to be surrounded, on average, by 5.6(2) oxygen atoms at a distance of 2.38 Å. The Ca coordination decreases to the unusually low value of 3.9(2) oxygen atoms at a distance of 2.40 Å at the eutectic composition. No additional Ca–O correlations are observed up to 2.7 Å, but longer bonds cannot be ruled out. The higher-r correlations are shown to be similar in the two glasses, suggesting that both Al and Ca may act as network formers. The results are compared to previous studies on splat-quenched glasses with compositions near the eutectic.