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A combination of inverse procedures is employed in the design of radio-frequency (RF) coils with specific examples in, but not restricted to, magnetic resonance imaging. The first inverse procedure is the use of functional methods for the optimization of coil characteristics subject to restrictions on the field behavior. Continuous current distributions are derived from analysis of the fields they are required to produce. To make use of these distributions at a desired frequency, the method of moments is applied as a second inverse procedure to a discretized version of the current distribution. The advantage of this hybrid technique is that it provides a computational algorithm for optimization of feeding, tuning, impedance matching and other aspects of RF coil design. A prototype RF coil has been built using the engineering values predicted by the theory. Experimental results including images acquired from the prototype coil are presented.