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Rees algebras of ideals having small analytic deviation

In this article we identify two large families of ideals of a Cohen-Macaulay (sometimes Gorenstein) local ring whose Rees algebras are Cohen-Macaulay. Our main results imply, for example, that if (R, M) is a regular local ring and P is a prime ideal of R such that P n is unmixed for all n ≥ 1, then the Rees algebra R[Pt] is Cohen-Macaulay if either dim(R/P) = 2, o< dim(R/P) = 3, R/P is Cohen-Macaulay, and R/P is integrally closed