Geological evidence indicates that the Sahara was glaciated by a large ice sheet c. 440 Ma ago. Two end-member theories have been proposed for the large-scale configuration of this ice mass. In the large ice-sheet hypothesis, the Sahara was covered by a continuous ice sheet that straddled North Africa–Arabia, South Africa and South America. In the small ice-sheet hypothesis, it has been argued that separate ice sheets developed in each of these areas. Taking these end-members and an ice sheet of intermediate dimensions, we investigate this problem, calculating likely ice volumes and the flux of ice to the ice margin. We find that the small ice sheet adequately accounts for the estimated magnitude of post-glacial transgression (c. 45–80 m) associated with ice-mass decay. Additionally, the notion of a North African–Arabian ice sheet within the small ice-sheet hypothesis is supported by an analysis of ice-stream fluxes across the Sahara, accounting for widespread heterogeneous flow within the ice sheet. This paper provides an independent check on the likely size and extent of Late Ordovician ice masses, with potential application to other Palaeozoic ice-sheet reconstructions.