This paper is concerned with the classical problem of optimal dividend payouts for a company. The author considers a company where surplus follows a diffusion process and whose objective is to maximize expected discounted dividend payouts to the shareholders, more exactly, to find a payout-scheme that maximizes the expected present value of all payouts until ruin occurs. The following restrictions are imposed: no dividends are allowed to be paid out unless surplus is at least

${b}_{0}$, and the surplus immediately after payment cannot be below

${b}_{0}$. Also, there is a level

${b}^{*}$ so that whenever surplus goes above

${b}^{*}$, the excess is paid out as dividends. If

${b}_{0}>{b}^{*}$, it is shown that an optimal restricted policy is to use a barrier strategy at

${b}_{0}$. This barrier is such that the probability of negative surplus within time

$T$ does not exceed prescribed

$\epsilon >0$. It is discussed how this

${b}_{0}$ can be calculated and a complete treatment is given when the surplus follows a Brownian motion with drift.