  In this paper, we find some general and efficient sufficient conditions for
the exponential convergence $W_{1,d}(P_t(x,\cdot), P_t(y,\cdot) )\le
Ke^{-\delta t}d(x,y)$ for the semigroup $(P_t)$ of one-dimensional diffusion.
Moreover some sharp estimates of the involved constants $K\ge 1, \delta>0$ are
provided. Those general results are illustrated by a series of examples.
