In this paper, we compare the performance of several speaker adaptation methods for a HMM-based Korean speech synthesis system with small amounts of adaptation data. According to objective and subjective evaluations, a hybrid method of constrained structural maximum a posteriori linear regression (CSMAPLR) and maximum a posteriori (MAP) adaptation shows better performance than other methods, when only five minutes of adaptation data are available for the target speaker. During the objective evaluation, we find that the duration models are insufficiently adapted to the target speaker as the spectral envelope and pitch models. To alleviate the problem, we propose the duration rectification method and the duration interpolation method. Both the objective and subjective evaluations reveal that the incorporation of the proposed two methods into the conventional speaker adaptation method is effective in improving the performance of the duration model adaptation.