Let K be an abelian number field contained in \({\mathbb{Q}}(\zeta_ N)\). \textit{A. Weil} [Trans. Am. Math. Soc. 73, 487-495 (1952; Zbl 0048.270); Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl. 1974, 1-14 (1974; Zbl 0367.10035)] showed how to use Jacobi sums attached to characters of order dividing N to produce Hecke characters whose values lie in K. The infinity types of these characters yield a Stickelberger ideal which annihilates the class group of K. The author and \textit{S. Lichtenbaum} [Comput. Math. 48, 55-87 (1983; Zbl 0513.12010)] generalized this construction to the situation where there is a finite collection of integers M, with \(K\subset {\mathbb{Q}}(\zeta_ M)\) for each M, and the Hecke character is formed by the Jacobi sums from characters of orders dividing the various values of M. In the present paper, the author removes the assumption that \(K\subset {\mathbb{Q}}(\zeta_ M)\), though K/\({\mathbb{Q}}\) is still assumed to be abelian. The condition implying that the construction yields a Hecke character leads to an enlarged Stickelberger ideal, which has been studied by \textit{W. Sinnott} [Invent. Math. 62, 181-234 (1980; Zbl 0465.12001)].