The plasma shape and location of a sharp boundary belt pinch is determined by the dimensions of the surrounding conducting shell and by thermodynamic parameters. It is shown that, except for simple scaling, there exists a one-parameter family of equilibria. The plasma shape is uniquely determined by initial parameters and wall current. The variation of the plasma shape during an adiabatic compression is calculated, as are plasma current, temperature, field strength, etc. As the compression ratio of the plasma is increased beyond two, the ratio of plasma height/width decreases to unity. For high compression ratios, the column cross-section becomes circular. Explicit solutions are obtained by conformal mapping.