We study the number of generators of ideals in regular rings and ask the question whether μ (I) < μ (I 2) if I is not a principal ideal, where μ (J) denotes the number of generators of an ideal J. We provide lower bounds for the number of generators for the powers of an ideal and also show that the CM-type of I 2 is ≥ 3 if I is a monomial ideal of height n in K [ x 1 , ... , x n ] and n ≥ 3.