An efficient aerodynamic design optimization method for. the compressible Euler equations is presented. A gradient-based optimization method is used to find the optimal design, in conjunction with a continuous adjoint sensitivity analysis method. To improve the efficiency of the design method, a tightly coupled algorithm based on a step-size estimation is proposed. The efficiency of the present method is demonstrated through drag minimizations of a wing and an airfoil. The result shows that the cost of the present method is significantly lower than that of the loosely coupled algorithm.