In this paper, we evaluate the performance of several objective measures in terms of predicting the quality of noisy speech enhanced by noise suppression algorithms. The objective measures considered a wide range of distortions introduced by four types of real-world noise at two SNRs by four classes of speech enhancement algorithms: spectral subtractive, subspace, statistical-model based and Wiener algorithms. The subjective quality ratings were obtained using the ITU-T P.835 methodology designed to evaluate the speech quality along three dimensions: signal distortion, noise distortion and overall quality. This paper reports the correlations of five common objective measures with these three subjective measures. Improvements to the PESQ measure are reported along with new composite objective measures.