  We introduce a class of $C^{1+\alpha}$ isolated nonuniformly hyperbolic sets
$\Lambda$ for which $\sup_{\mu \in {\mathcal M}_f}\{h(\mu) - \chi^+(\mu)\}$
equals the rate of escape from $\Lambda$, where $\chi^+(\mu)$ is the average of
the sum of positive Lyapunov exponents counted with their multiplicity.
