There has been much recent interest in adapting data mining algorithms to time series databases. Many of these algorithms need to compare time series. Typically some variation or extension of Euclidean distance is used. However, as we demonstrate in this paper, Euclidean distance can be an extremely brittle distance measure. Dynamic time warping (DTW) has been suggested as a technique to allow more robust distance calculations, however it is computationally expensive. In this paper we introduce a modification of DTW which operates on a higher level abstraction of the data, in particular, a piecewise linear representation. We demonstrate that our approach allows us to outperform DTW by one to three orders of magnitude. We experimentally evaluate our approach on medical, astronomical and sign language data.