  This paper studies large dam models where the difference between lower and
upper levels, $L$, is assumed to be large. Passage across the levels leads to
damage, and the damage costs of crossing the lower or upper level are
proportional to the large parameter $L$. Input stream of water is described by
compound Poisson process, and the water cost depends upon current level of
water in the dam. The aim of the paper is to choose the parameters of output
stream (specifically defined in the paper) minimizing the long-run expenses.
The particular problem, where input stream is ordinary Poisson and water costs
are not taken into account, has been studied in [Abramov, \emph{J. Appl.
Prob.}, 44 (2007), 249-258]. The present paper addresses the question
\textit{How does the structure of water costs affect the optimal solution?}
Under natural assumptions we prove an existence and uniqueness of a solution
and study the case of linear structure of the costs.
