This work describes three new developments in the design and use of gradient coils in MRI. A novel gradient coil, consisting of folded loop current path has been developed. In this design, the current return paths for the inner coil are folded over onto the outer screening coil and both coils have the same length. This sort of design will potentially allow more efficient short coils with better screening to be designed. Mathematical expressions for the magnetic field produced by such coils have been developed and tested by comparison with the results of field calculations based on the elemental form of the Biot-Savart expression. A small prototype coil has been built and tested. The field variation which it produces is in good agreement with that calculated from the wire paths.