We analyze and quantify the capabilities and limitations of a double-conjugate adaptive-optics system. In the proposed system the contribution of two turbulent layers is treated separately, with Rayleigh guide stars for the bottom layer, sodium guide stars for the top layer, and two adaptive mirrors conjugate to the respective layers. The system substantially increases the compensated field of view. We give calculated results for the estimated number of guide stars needed, the wave-front sensor, and the adaptive-mirror resolution. Simulation results are also presented, and the residual error remaining after correction in our proposed system is compared with a conventional single-adaptive-mirror system.