Chiral perturbation theory is a very useful framework for testing the standard model in processes where long-distance effects are expected to play an essential rôle. We analyze the rare K decays K0→γℓ+ℓ−, K+→π+γ3 and KL→π0ℓ+ℓ− in the effective chiral formulation of the standard model. These processes, like the decays K0→γγ, K+→π+ℓ+ℓ−, KS→π0ℓ+ℓ− and K0→π0γγ discussed in previous work, have the property that the corresponding amplitudes vanish to lowest order in chiral perturbation theory. Precise predictions for decay rates and spectra are made in terms of a few coupling constants not restricted by softly broken chiral symmetry alone. Special consideration is given to various possible tests of CP noninvariance in these decays, in particular to effects due to intrinsic CP violation in the amplitudes. We find that chiral perturbation theory correlates different CP-violating observables such as the charge asymmetries in K±→π±γγ and K±→π±ℓ+ℓ−, the one-photon exchange contribution to KL→π0e+e− and the transverse polarization in KL →π0μ+μ−. Detailed numerical results are shown.