Abstract : The Canonical Polyadic (CP) decomposition of a tensor is difficult to compute. Even algorithms computing the best rank-one approximation are not entirely satisfactory. And deflation approaches (successive rank-1 tensor approximations) do not work for tensors. However, there are cases where successive rank-1 matrix approximations can help in computing the CP decomposition. This is what we investigate in this talk. In particular, we analyze the cases where loading matrices are banded and structured, e.g. Toeplitz or Hankel.