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The objective of partially adaptive array design is to reduce the number of adaptive weights without significantly degrading the performance of the adaptive array. Previous work includes numerical techniques for approximately minimizing the average generalized sidelobe canceller (GSC) output power for a desired number of adaptive weights, where the average is over a range of jammer parameters. Our new "power-space method" also attempts to minimize the average GSC output power, but under a constraint that the reduced-dimensional solutions for all of the scenario trials lie in the same subspace. This constraint allows us to use the singular value decomposition to get the rank-reducing transformation, thereby simplifying the optimization problem. Using computer simulation, we show that our transformation yields lower output power in comparison with a previously reported example that used the numerical methods. The simplicity of the method allows large ranges of jammer parameters to be considered, Using our transformation, we consider how closely the reduced-rank solutions match the full-rank solutions and how the quality of this match relates to the output power of the partially adaptive array.