  We propose a new approximation for the distribution of the time of the first
crossing of a high level $u$ by random process $\homV{s}-cs$, where $\homV{s}$,
$s>0$, is compound renewal process and $c>0$. It significantly outperforms the
existing approximations, particularly in the region around the critical point
$c=\cS$ which separates processes with positive and negative drifts. This
approximation is tightly related to generalized inverse Gaussian distributions.
