In the setting of Hall and Murphy (2000, 2002), we can observe that the executive’s incentives to increase the stock price can be very low on some ranges of the stock price. So we propose a new stock option compensation scheme whose payoffs are concave with respect to the stock price when the stock price at option’s maturity exceeds the strike price. This kind of options allows the executive to have greater incentives compared with the traditional option model. Hall and Murphy (2000, 2002) also analyze the incentive effects only on the grant date of the options. We find that the incentives at some time (after the grant date) might not be optimal even though the firm chose the moneyness of the option that gave the executive the optimal incentives on the grant date.