A review of 127 shelf-margin accretion segments from 24 margins worldwide suggests that sediment flux can be low or high, that shelf accommodation can be low, medium, or high, and that climatic conditions can be Icehouse or Greenhouse. The interplay of these three variables yields four main Greenhouse margins and six main Icehouse margins, and thus has a fundamental control on shelf-margin architectural styles, providing new tools for predicting internal architecture of deep-water systems. In Greenhouse settings, there is commonly a strong supply drive (because of higher temperatures, more variable precipitation and higher sediment discharge), but only modest shelf accommodation (because of low-frequency and low-amplitude eustatic sea-level changes). Low shelf accommodation is able to deliver significant volumes of sand sourced from either low or high sediment supply areas to deep-water environments, and residence time for deltas at Greenhouse margins is likely to be relatively long because of the low amplitude of Greenhouse sea-level changes. Medium accommodation, in contrast, may overwhelm any low sediment supply, but could be partly overwhelmed by high sediment supply, which, in turn, can inhibit fans or encourage highstand fans. In Icehouse settings, there is a strong, cross-shelf accommodation drive created by high-frequency and high-amplitude eustatic sea-level changes, thus causing significant and frequently repeated transits of river mouths and deltas across the shelf. Sandy basin-floor fans created by low accommodation are predicted with either high or low sediment flux. Both medium and high accommodation can be volumetrically overwhelmed by high sediment supply, which, in turn, cause greater volumes of sediment storage on the shelf, resulting in volumetrically less significant highstand or transgressive submarine fans. However, a low supply may barely allow deltas to reach the shelf edge, causing the deep-water areas to be dominantly muddy.