The current interpretation of excitation energy transfer (EET) processes in natural photosynthesis generally relies on Kasha’s rule, suggesting that internal conversion (IC) processes usually outpace any EET between higher excited states. It is, however, known from research on artificial systems that Kasha’s rule does not apply to many dyes, especially when found in assembled clusters analogous to photosynthetic chlorophyll (Chl)-protein complexes. In this contribution, a semiempirical Förster-type model is applied to otherwise well-investigated pigments of natural photosynthesis (Chls a , b , c1 and various carotenoids). Strong potential for anti-Kasha processes is identified in all investigated pigments, based on their high Coulomb coupling elements, similar to compounds with already known anti-Kasha properties. The pigments are further found to form strongly delocalized excitons, especially between the higher excited states usually responsible for anti-Kasha pathways. Test calculations with different pigment compositions for various natural light harvesting complexes (LHCII, CP24, CP26, CP29, FCP) demonstrate how the higher band EET network and absorbance could be affected by the presence of accessory pigments: Chl a -only networks should perform anti-Kasha EET, but this is suppressed by the presence of accessory pigments via several mechanisms (exciton disruption, spectral competition, energy sinks and fast, non-Chl a IC). The apparent “special” behavior of photosynthetic systems is thus resolved as the result of pigment mixtures.