  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.
