The construction of fixed-width confidence intervals for an unknown population parameter is often based on the normal approximation of an appropriate statistic. In this paper we follow a different approach using bootstrap appro¬ximations, which are known to have a high degree of accuracy. It is expected that such an approximation leads to better results, at least in the second order behaviour.In order to avoid computationally very costly procedures,inherent to a fully sequential method,we implement the bootstrap ideas in a three-stage procedure.Simulation results illustrate the performance of the proposed procedure for small and moderate sample sizes.To support the method we establish some basic asymptotic properties.