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The main purpose of this article is to increase the efficiency of the tools introduced in [B.Mg. 98] and [B.Mg. 99], namely integration of meromorphic cohomology classes, and to generalize the results of [B.Mg. 99]. They describe how positivity conditions on the normal bundle of a compact complex submanifold Y of codimension n + 1 in a complex manifold Z can be transformed into positivity conditions for a Cartier divisor in a space parametrizing n−cycles in Z . As an application of our resultsdoi:10.4310/ajm.2004.v8.n1.a13 fatcat:kte6h7giefb6fnqzjwrlad6f3a