The inverse first-passage problem for a Wiener process $(W_t)_{t\ge0}$ seeks
to determine a function $b{}:{}\mathbb{R}_+\to\mathbb{R}$ such that
\[\tau=\inf\{t>0| W_t\ge b(t)\}\] has a given law. In this paper two methods
for approximating the unknown function $b$ are presented. The errors of the two
methods are studied. A set of examples illustrates the methods. Possible
applications are enlighted.