The optimal dividend problem goes back to a paper that Bruno De Finetti presented to the International Congress of Actuaries in New York (1957). For a stock company which pays dividends to its shareholders, what is the strategy that maximizes the expectation of the discounted dividends (until possible ruin)? Jeanblanc-Picqué and Shiryaev (1995) and Asmussen and Taksar (1997) solved the problem by modeling the aggregate net income of the company by a Wiener process and imposing the condition of a bounded dividend rate. Here we study the problem with the Wiener process generalized to a compound Poisson process.