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| In this work we study a family of partially hyperbolic horseshoes introduced by L. Diaz {\it et al} [Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes,
{\it Ergod. Th. and Dynamical Systems} \textbf{29}, 2009]. In [\textit{Equilibrium States for partially hyperbolic horseshoes}.
Ergod. Th. and Dynamical Systems. \textbf{31} 2011], R. Leplaideur {\it et al} proved the existence of equilibrium states for the diffeomorphisms $F$ in this family, associated to continuous potentials. They also proved the existence of a spectral gap associated to the central Lyapunov exponents, and that, for a positive value of $t_0$, the smooth potencial $t_0\log || DF |_{E^c}||$ admits at least two equilibrium states. Here we prove the uniqueness of equilibrium states for the class of Holder-continuous potentials with small variation, wich includes $t_0\log || DF |_{E^c}||$, for small values of $t$. |
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