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Two new algorithms are presented for the segmentation of a white Gaussian-distributed time series having unknown but piecewise-constant variances. The first "sequential/minimum description length (MDL)" idea includes a rough parsing via the GLR, a penalization of segmentations having too many parts via MDL, and an optional refinement stage. The second "Gibbs sampling" approach is Bayesian and develops a Monte Carlo estimator. From simulation, it appears that both schemes are very accurate in terms of their segmentation but that the sequential/MDL approach is orders of magnitude lower in its computational needs. The Gibbs approach can, however, be useful and efficient as a final post-processing step. Both approaches (and a hybrid) are compared with several algorithms from the literature.