Speech enhancement algorithms aim to improve the quality and intelligibility of noise corrupted speech, through spectral or temporal modifications. Most of the existing speech enhancement algorithms achieve this by modifying the magnitude spectrum alone, while keeping the phase spectrum intact. In the current work, both phase and magnitude spectra are modified to enhance noisy speech using a multi-level speech enhancement technique. Proposed phase compensation (PC) function achieves first-level enhancement by modifying the phase spectrum alone. Second-level enhancement performs energy redistribution in the phase compensated speech signal to make weak speech and non-speech regions highly contrastive. Energy redistribution from the energy-rich voiced to the weak unvoiced regions is carried out using adaptive power law transformation (APLT) technique by optimizing the parameters with a total energy constraint employing particle swarm optimization algorithm. Log MMSE technique with a novel speech presence uncertainty (SPU) estimation method is proposed for third-level enhancement. The compensated phase spectrum and the magnitude spectrum estimated using log MMSE, with proposed SPU estimation (log MMSE + proposed SPU), are used to reconstruct the enhanced speech signal. The proposed speech enhancement technique is compared with recent speech enhancement techniques that estimate both magnitude and phase, for various noise levels (−5 to +5 dB), in terms of objective and subjective measures. It is observed that the proposed technique improves signal quality and maintains or improves intelligibility under stationary, and non-stationary noise conditions.