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The goal of voice conversion is to transform a sentence said by one speaker, to sound as if another speaker had said it. The classical conversion based on a Gaussian Mixture Model and several other schemes suggested since, produce muffled sounding outputs, due to excessive smoothing of the spectral envelopes. To reduce the muffling effect, enhancement of the Global Variance (GV) of the spectral features was recently suggested. We propose a different approach for GV enhancement, based on the classical conversion formalized as a GV-constrained minimization. Listening tests show that an improvement in quality is achieved by the proposed approach.