The convection of cold water in the vicinity of its density maximum in a rectangular enclosure is studied in the limit of small Rayleigh number. Results for the stream function (to lowest order) and the first corrections (for convective effects) to the temperature field and heat transfer are obtained. Results are discussed in the context of a single parameter, which fixes the orientation of the wall temperatures with respect to the extremum temperature. The effects of changing the enclosure aspect ratio are also discussed.