Sensitivity has become a basic concept in biology, but much less is known about its tuning, probably because allosteric cooperativity, the best known mechanism of sensitivity, is determined by rigid conformations of interacting molecules and is thus difficult to tune. Reversible covalent modification (RCM), owing to its systems-level ingenuity, can generate concentration based, tunable sensitivity. Using a mathematical model of regulated RCM, we find sensitivity tuning can be decomposed into two orthogonal modes, which provide great insights into vital biological processes such as tissue development and cell cycle progression. We find that decoupling of the two modes of sensitivity tuning is critical to fidelity of cell fate decision; the decoupling is thus important in development. The decomposition also allows us to solve the 'wasteful degradation conundrum' in budding yeast cell cycle checkpoint, which further leads to discovery of a subtle but essential difference between positive feedback and double negative feedback. The latter guarantees revocability of stress-induced cell cycle arrest; while the former does not. By studying concentration conditions in the system, we extend applicability of ultrasensitivity and explain the ubiquity of reversible covalent modification.