Kinases and phosphatases work antagonistically to control the behaviour of individual substrate molecules. This can be incorrectly extrapolated to imply that they also work antagonistically on the signals or processes that these molecules control. In fact, in many situations kinases and phosphatases work together to positively drive signal responses. We explain how this 'cooperativity' is critical for setting the amplitude, localisation, timing, and shape of phosphorylation signals. We use mitosis to illustrate why these properties are important for controlling mitotic entry, sister chromatid cohesion, kinetochore-microtubule attachments, the spindle assembly checkpoint, mitotic spindle elongation, and mitotic exit. These examples provide a rationale to explain how complex signalling behaviour could rely on similar types of integration within many other biological processes.