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A phoneme class based speech enhancement algorithm is proposed that is derived from the family of constrained iterative enhancement schemes. The algorithm is a Rover based solution that overcomes three limitations of the iterative scheme. It removes the dependency of the terminating iteration, employs direct phoneme class constraints, and achieves suppression of audible noise. In the Rover scheme, the degraded utterance is partitioned into segments based on class, and class specific constraints are applied on each segment using a hard decision method. To alleviate the effect of hard decision errors, a GMM based maximum likelihood (ML) soft decision method is also introduced. Performance evaluation is done using Itakura-Saito, segSNR, and PESQ metrics for four noise types at two SNRs. It is shown that the proposed algorithm outperforms other baseline algorithms like Auto-LSP and log-MMSE for all noise types and levels and achieves a greater degree of consistency in improving quality for most phoneme classes.