  We give a bound on the H-constants of configurations of smooth curves having
transversal intersection points only on an algebraic surface of non-negative
Kodaira dimension. We also study in detail configurations of lines on smooth
complete intersections $X \subset \mathbb{P}^{n+2}_{\mathbb{C}}$ of
multi-degree $d=(d_1, \dots, d_n)$, and we provide a sharp and uniform bound on
their H-constants, which only depends on $d$.
