Sequence compression is one of the most promising tools for strengthening pseudo-random generators used in stream ciphers. Indeed, adding compression components can thwart algebraic attacks aimed at LFSR-based stream ciphers. Among such components are the Shrinking Generator and the Self-Shrinking Generator, as well as recent variations on Bit-Search-based decimation. We propose a general model for compression used to strengthen pseudo-random sequences. We show that there is a unique (up to length-preserving permutations) construction that reaches an optimal trade-off between output rate and security against several attacks.