Intramolecular Förster-type excitation energy transfer (FRET) processes in a series of first-generation polyphenylene dendrimers substituted with spatially well-separated peryleneimide chromophores and a terryleneimide energy-trapping chromophore at the rim were investigated by steady-state and time-resolved fluorescence spectroscopy. Energy-hopping processes among the peryleneimide chromophores are revealed by anisotropy decay times of 50--80 ps consistent with a FRET rate constant of k(hopp) = 4.6 ns(-1). If a terryleneimide chromophore is present at the rim of the dendrimer together with three peryleneimide chromophores, more than 95% of the energy harvested by the peryleneimide chromophores is transferred and trapped in the terryleneimide. The two decay times (tau(1) = 52 ps and tau(2) = 175 ps) found for the peryleneimide emission band are recovered as rise times at the terryleneimide emission band proving that the energy trapping of peryleneimide excitation energy by the terryleneimide acceptor occurs via two different, efficient pathways. Molecular- modeling-based structures tentatively indicate that the rotation of the terryleneimide acceptor group can lead to a much smaller distance to a single donor chromophore, which could explain the occurrence of two energy-trapping rate constants. All energy-transfer processes are quantitatively describable with Förster energy transfer theory, and the influence of the dipole orientation factor in the Förster equation is discussed.