We show that the chromatic index of a hypergraph $\mathcal{H}$ satisfies Berge-Füredi conjectured bound $\mathrm{q}(\mathcal{H})\le Δ([\mathcal{H}]_2)+1$ under certain hypotheses on the antirank $\mathrm{ar}(\mathcal{H})$ or on the maximum degree $Δ(\mathcal{H})$. This provides sharp information in connection with Erdős-Faber-Lovász Conjecture which deals with the coloring of a family of cliques that intersect pairwise in at most one vertex.
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