Tests of CPT

The ongoing experimental efforts in the high energy and high precision communities keep providing evidence for CPT, a fundamental symmetry holding in any local Lorentz invariant theory. We suggest possible interconnections between different CPT violating parameters. Specifically, the very precise test of CPT in the $K^0-\bar K^0$ system suggests--though definitely does not imply--that CPT violations in other observable parameters (mass, width, charge, magnetic moments, etc.) are much smaller than the directly measured bounds.