SummaryBootstrap techniques have been used to construct confidence bands in nonparametric regression problems (Härdle&Bowman, 1988). Yet the required simulation is generally computationally intensive and therefore makes it difficult to conduct further investigations. In this paper, two saddlepoint methods are considered as alternatives to the naive simulation procedure. Some improvements to Härdle&Bowman's bootstrap method are suggested. The improvements are numerically verified using these efficient and accurate analytic method