Dirty Paper Trellis Codes (DPTC) watermarking, published in 2004, is a very efficient high rate scheme. Nevertheless, it has two strong drawbacks: its security weakness and its CPU computation complexity. We propose an embedding space at least as secure and a faster embedding. The embedding space is built on the projections of some wavelet coefficients onto secret carriers. It keeps a good security level and has also good psycho-visual properties. The embedding is based on a dichotomous rotation in the Cox, Miller and Boom Plane. It gives better performances than previous fast embedding approaches. Four different attacks are performed and revealed good robustness and rapidity performances.