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We consider MIMO systems with flat fading under the quasi-static model, where the block size is on the order of tens of symbols. A relatively short block is required in mobile environments if the quasi-static model is to remain valid. To overcome the short data size, algorithms that exploit both training and signal properties are of interest. We focus on exploitation of training (semi-blind) and constant modulus (CM) signaling, and develop appropriate Cramer-Rao bounds (CRB) for these cases. The CRB provide insight into the level of training required, and show that in many scenarios increasing the number of training beyond about five symbols adds little new information. The analysis includes the impact of reduced channel rank on source estimation. The combination of semi-blind and CM is particularly informative for the short data sizes we have examined. We describe several algorithms, and compare simulated performance with the CRB on channel and source estimation. Both blind (ACMA) and semi-blind (scoring) approaches that exploit the CM property are compared. Using ACMA as a blind initialization, the scoring estimates can approach the semi-blind CM CRB.