Abstract Data from the CPLEAR experiment, together with the most recent world averages for some of the neutral-kaon parameters, were constrained with the Bell–Steinberger (or unitarity) relation, allowing the T-violation parameter Re( ϵ) and the CPT-violation parameter Im( δ) of the neutral-kaon mixing matrix to be determined with an increased accuracy: Re( ϵ)=(164.9±2.5)×10 −5, Im( δ)=(2.4±5.0)×10 −5. Moreover, the constraint allows the CPT-violation parameter for the neutral-kaon semileptonic decays, Re( y), to be determined for the first time. The ΔS≠ ΔQ parameters Re( x −) and Im( x +) are given with an increased accuracy. The quantity Re( y+ x −), which enters the T-violation CPLEAR asymmetry previously published, is determined to be (−0.2±0.3)×10 −3. The value obtained for Re( δ) is in agreement with the one resulting from a previous unconstrained fit and has a slightly smaller error.