Basic constraints on the dense water formation rate and circulation resulting from cooling around an island are discussed. The domain under consideration consists of an island surrounded by a shelf, a continental slope, and a stratified ocean. Atmospheric cooling over the shelf forms a dense water that penetrates down the sloping bottom into the stratified basin. Strong azimuthal flows are generated over the sloping bottom as a result of thermal wind. Thermally direct and indirect mean overturning cells are also forced over the slope as a result of bands of convergent and divergent Reynolds stresses associated with the jets. The Coriolis force associated with the net mass flux into the downwelling region over the slope is balanced by these nonlinear terms, giving rise to a fundamentally different momentum budget than arises in semienclosed marginal seas subject to cooling. A similar momentum balance is found for cases with canyons and ridges around the island provided that the terms are considered in a coordinate system that follows the topography. Both eddy fluxes and the mean overturning cells are important for the radial heat flux, although the eddy fluxes typically dominate. The properties of the dense water formed over the shelf (temperature, diapycnal mass flux) are predicted well by application of baroclinic instability theory and simple heat and mass budgets. It is shown that each of these quantities depends only on a nondimensional number derived from environmental parameters such as the shelf depth, Coriolis parameter, offshore temperature field, and atmospheric forcing.