Techniques are described for the design of shielded gradient coils for superconducting MRI systems. These design methods are suited for constructing the most efficient gradient coil that meets a specified homogeneity requirement. Tradeoffs in coil design of efficiency with coil size and gap size are discussed. Residual eddy currents from coils constructed with a finite number of wires are calculated and give guidelines for the construction of efficient, whole-body gradient coils.