In recent work on experimental tests of quantum-gravity-motivated phenomenological models, a significant role has been played by the so-called "κ" deformations of Poincaré symmetries. Sensitivity to values of the relevant deformation length λ as small as 5×10-33 m has been achieved in recent analyses comparing the structure of κ-Poincaré symmetries with data on the gamma rays we detect from distant astrophysical sources. We investigate violations of CPT symmetry which may be associated with κ-Poincaré in the physics of the neutral-kaon system. A simple estimate indicates that experiments on the neutral kaons may actually be more λ-sensitive than the corresponding astrophysical experiments, and may already allow to probe values of λ of order the Planck length.