Sanitizable signature schemes allow a semi-trusted entity to modify some specific portions of a signed message while keeping a valid signature of the original off-line signer. In this paper, we give a new secure sanitizable signature scheme which is, to the best of our knowledge, the most efficient construction with such a high level of security. We also enhance the Brzuska et al. model on sanitizable signature schemes by adding new features. We thus model the way to limit the set of possible modifications on a single block, the way to force the same modifications on different admissible blocks, and the way to limit both the number of modifications of admissible blocks and the number of versions of a signed message. We finally present two cryptanalysis on proposals for two of these features due to Klonowski and Lauks at ICISC 2006 and propose some new practical constructions for two of them. Keywords. Sanitizable signature, chameleon hash, accumulator scheme.