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The problem of separating out the signals for multiple speakers from a single mixed recording has received considerable attention in recent times. Most current techniques are based on the principle of masking: in order the separate out the signal for any speaker, frequency components that are not believed to belong to that speaker are suppressed. The signals for the various speakers are reconstructed from the partial spectral information that remains. In this paper we present a different kind of technique -- one that attempts to estimate all spectral components for the desired speaker. Separated signals are derived from the complete spectral descriptions so obtained. Experiments show that this method results in superior reconstruction to masking based reconstruction.