Given a compact connected set E in the unit disk B² , we give a new upper bound for the conformal capacity of the condenser (B², E)  in terms of the hyperbolic diameter t of E. Moreover, for t >0, we construct a set of hyperbolic diameter t and apply novel numerical methods to show that it has larger capacity than a hyperbolic disk with the same diameter. The set we construct is called a Reuleaux triangle in hyperbolic geometry and it has constant hyperbolic width equal to t.