The degree of influence of noise over phonemes is not uniform since it is dependent on their distinct acoustic properties. In this study, the problem of selectively enhancing speech based on broad phoneme classes is addressed using Auto-(LSP), a constrained iterative speech enhancement algorithm. Multiple enhanced utterances are generated for every noisy utterance by varying the Auto-LSP parameters. The noisy utterance is then partitioned into segments based on broad level phoneme classes, and constraints are applied on each segment using a hard decision solution. To alleviate the effect of hard decision errors, a Gaussian mixture model (GMM)-based maximum-likelihood (ML) soft decision solution is also presented. The resulting utterances are evaluated over the TIMIT speech corpus using the Itakura-Saito, segmental signal-to-noise ratio (SNR) and perceptual evaluation of speech quality (PESQ) metrics over four noise types at three SNR levels. Comparative assessment over baseline enhancement algorithms like Auto-LSP, log-minimum mean squared error (log-MMSE), and log-MMSE with speech presence uncertainty (log-MMSE-SPU) demonstrate that the proposed solution exhibits greater consistency in improving speech quality over most phoneme classes and noise types considered in this study.