Coastal polynyas are key formation regions for Dense Shelf Water (DSW) that ultimately contribute to the ventilation of the ocean abyss. However, not all polynyas form DSW. We examine how the physiographic setting, water-mass distribution and transformation, water column stratification, and sea-ice production regulate DSW formation in four East Antarctic coastal polynyas. We use a salt budget to estimate the relative contribution of sea-ice production, lateral advection, and vertical entrainment to the monthly change in salinity in each polynya. DSW forms in Mackenzie polynya due to a combination of physical features (shallow water depth and a broad continental shelf) and high sea-ice production. Sea-ice formation begins early (March) in Mackenzie polynya, counteracting fresh advection and establishing a salty mixed layer in autumn that preconditions the water column for deep convection in winter. Sea ice production is moderate in the other three polynyas, but saline DSW is not formed (a fresh variety is formed in the Barrier polynya). In the Shackleton polynya, brine rejection during winter is insufficient to overcome the very fresh autumn mixed layer. In Vincennes Bay, strong inflow of modified Circumpolar Deep Water stratifies the water column, hindering deep convection and DSW formation. Our study highlights that DSW formation in a given polynya depends on a complex combination of factors, some of which may be strongly altered under a changing climate, with potentially important consequences for the ventilation of the deep ocean, the global meridional overturning circulation, and the transport of ocean heat to Antarctic ice shelves.