This paper presents the repeated filtering method for finding a smoothed, Bayesian estimate of the path of a stochastic process over a time interval [0, T] when one has used a particle filter to estimate the state of the process. It provides good resolution over [0, T], is easy to implement, and can be used with any sequential importance resampling particle filter regardless of the probabilistic model employed by the stochastic process. Repeated filtering is general, powerful, and simple. It does not require the restrictive assumptions or complex calculations of other methods. It is suitable for real-time operational use in complex situations. We demonstrate the method on two single-target tracking examples. The second of these tracking examples is very difficult to solve by any other method known to us. We then apply re-peated filtering to a standard nonlinear time series model that has been used extensively for testing numerical filtering techniques. To further illustrate the power of repeated filtering, we show how adding reflecting boundaries to this time series creates a process that is difficult to smooth with existing techniques but simple with repeated filtering.