The purpose of this paper is to introduce and examine two alternative, although similar, approaches to the Moving Blocks and subsampling Bootstraps to bootstrapping the estimator of the parameters for time series regression models. More specifically, the first bootstrap is based on resampling from the normalised discrete Fourier transform of the residuals of the model, whereas the second is from the residuals of the model itself. It is shown that the bootstraps are asymptotically valid under quite mild conditions. As a consequence of the result we are able to eleminate the apparent drawback of choosing the block length in empirical examples. A small Monte Carlo study of finite sample performance is included.