User-oriented computer programmes in FORTRAN IV for discrete least pth approximation with a single specified function, and more generalized discrete least pth approximation with various specifications, which may also be used for non-linear programming, are presented. Values of p up to 10" can be used successfully in conjunction with efficient gradient minimization algorithms such as the Fletcher-Powell method and a method due to Fletcher. It has been demonstrated how efficiently extremely near minimax results can be achieved on a discrete sot of sample points using this approach and the programmes written verify this. The programmes may be applied to a wide variety of design problems with a wide range of specifications. They are suitable for electrical network and system design and such problems as filter design.