Recent structural data revealed that the CP29 protein of higher plant photosystem II (PSII) contains 13 chlorophylls (Chl's) per complex (Pan et al. Nat. Struct. Mol. Biol. 2011, 18, 309), i.e., five Chl's more than in the predicted CP29 homology-based structure model (Bassi et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 10056). This lack of consensus presents a constraint on the interpretation of CP29 optical spectra and their underlying electronic structure. To address this problem, we present new low-temperature (5 K) absorption, fluorescence, and hole-burned (FIB) spectra for CP29 proteins from spinach, which are compared with the previously reported data. We focus on excitation energy transfer (EET) and the nature of the lowest-energy state(s). We argue that CP29 proteins previously studied by HB spectroscopy lacked at least one CM a molecule (i.e., a615 or a611), which along with CM a612 contribute to the lowest energy state in more intact CP29, and one CM b (most likely b607). This is why the low-energy state and fluorescence maxima reported by Pieper et al. (Photochem. Photobiol 2000, 71, 574) were blue-shifted by similar to 1 nm, the low-energy state appeared to be highly localized on a single CM a molecule, and the position of the low-energy state was independent of burning fluence. In contrast, the position of the nonresonant FIB spectrum shifts blue with increasing fluence in intact CP29, as this state is strongly contributed to by several pigments (i.e., a611, a612, a615, and a610). Zero-phonon hole widths obtained for the Chl b band at 638.5 nm (5 K) revealed two independent Chl b -> Chl a BET times, i.e., 4 +/- 0.5 and 0.4 +/- 0.1 ps. The latter value is a factor of 2 faster than previously observed by FIB spectroscopy and very similar to the one observed by Gradinaru et al. (J. Phys. Chem. B 2000, 104, 9330) in pump-probe experiments. EET time from 650 tun Chl b -> Chl a and downward EET from Chl(s) a state(s) at 665 nm occurs in 4.9 +/- 0.7 ps. These findings provide important constraints for excitonic calculations that are discussed in the accompanying paper (part II, DOI 10.1021/jp4004278).