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We continue the work of Shelah and Casanovas on the cardinality of families of pairwise inconsistent types in simple theories. We prove that, in a simple theory, there are at most ${\lambda }^{<\kappa \left(T\right)}+2^{\mu +\left|T\right|}$ pairwise inconsistent types of size μ over a set of size λ. This bound improves the previous bounds and clarifies the role of κ(T). We also compute exactly the maximal cardinality of such families for countable, simple theories. The main tool is the fact that, in simple theories, the collection of nonforking extensions...