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Various speech enhancement techniques rely on the knowledge of the clean signal and noise statistics. In practice, however, these statistics are not explicitly available, and the overall enhancement accuracy critically depends on the estimation quality of the unknown statistics. The estimation of noise (and speech) statistics is particularly challenging under non-stationary noise conditions. In this respect, subspace-based approaches have been shown to provide a good tracking vs. final misadjustment tradeoff. Subspace-based techniques hinge critically on both rank-limited and spherical assumptions of the speech and the noise DFT matrices, respectively. The speech rank-limited assumption was previously experimentally tested and validated. In this paper, we will investigate the structure of nuisance sources. We will discuss the validity of the spherical assumption for a variety of nuisance sources (environmental noise, reverberation), and preprocessing (overlapping segmentation).