We introduce new possibilities to control the application of rules based on the preceding applications, which can be de ned in a general way for (hierarchical) P systems and the main known derivation modes. Computational completeness can be obtained even for one-membrane P systems with non-cooperative rules and using both activation and blocking of rules, especially for the set modes of derivation. When we allow the application of rules to in uence the application of rules in previous derivation steps, applying a non-conservative semantics for what we consider to be a derivation step, we can even \go beyond Turing".