  Given a finite set \sigma of the unit disc \mathbb{D}=\{z\in\mathbb{C}:,\,|
z|<1\} and a holomorphic function f in \mathbb{D} which belongs to a class X,
we are looking for a function g in another class Y (smaller than X) which
minimizes the norm ||g||_{Y} among all functions g such that
g_{|\sigma}=f_{|\sigma}. For Y=H^{\infty}, and for the corresponding
interpolation constant c(\sigma,\, X,\, H^{\infty}), we show that c(\sigma,\,
X,\, H^{\infty})\leq a\phi_{X}(1-\frac{1-r}{n}) where n=#\sigma,
r=max_{\lambda\in\sigma}|\lambda| and where \phi_{X}(t) stands for the norm of
the evaluation functional f\mapsto f(\lambda) on the space X. The upper bound
is sharp over sets \sigma with given n and r.
