The method of surrogate testing is frequently employed in time series analysis for the detection of nonlinearities in data, and for constructing an time series ensembles preserving certain statistical properties of the original dataset. In the framework of information causality, surrogates are used to test the statistical signi cance of directional information flow between time series. Here, we present two new methods for generating uni- and multivariate surrogate data: attractor density invariant surrogates, and dynamically invariant surrogates. The transfer operator derived surrogates are computationally expensive to compute, but are advantageous when dealing with short time series, because they may be used to extend short and noisy data sets to produce more reliable statistics. As an example, we demonstrate that attractor dimension estimation from short, sparsely sampled time series may be signi cantly improved using these new surrogate methods.