This paper reconstructs the characteristics of rivers which deposited proglacial fluvial sediments in east-central Scotland during the Late Devensian. Sediment depositional architecture and geometry, together with the relationship between high-stage and falling and low-stage depositional elements, were used to relate the proglacial sediments to the glacial meltwater discharge regime. The proglacial river systems studied were dominated by ‘normal’ ablation controlled discharge, rather than by high magnitude flood events. Consequently there is a great deal of spatial and vertical variability. Deposition occurred during short intervals of rapid aggradation, so that relatively fine-grained falling-stage sediments, as well as coarser, bar-core sediments are well preserved. Models relating the characteristics of the final deposit to the nature of the river are presented. These emphasise the role of stage changes and aggradation rates in controlling sediment architecture in braided fluvial deposits.