The reactions Li7(He3, p)Be9, B10(He3, p)C12, and B11(He3, p)C13 have been used to study the level structures of Be9, C12, and C13, respectively. Levels of Be9 were observed at 1.83, 2.43, 3.1, and 4.8 Mev. Observations of the group corresponding to 1.83 Mev at different angles are consistent with the assumption of a level in Be9 although a 3-body spectrum from He3+Li7-->Be8+n+p could also fit the data. With the groups corresponding to the well-known C12 levels at 4.43, 7.65, 9.61, and 16.10 Mev used as calibrations, other levels were observed at 10.90, 11.84, 12.69, 13.30, 14.05, 14.97, 15.62, and 16.57 Mev. For the 7.65-Mev level ΓγΓα<1.4% if the level emits a single γ ray of 7.65 Mev, and ΓγΓα<0.9% if there is a cascade through the 4.43-Mev state as it would if it were a O+ leve. A proton group due to an α-particle level, predicted to lie at 5.53 Mev in C12, was not found and must be more than 4000 times weaker than the proton group leading to the 4.43-Mev level. Rough estimates of ΓγΓα for the 14.97- and 12.69-Mev levels are 50+/-25% and 3+/-1%, respectively. With the well-known C13 levels up to 6.87 Mev being used as calibrations, other levels were observed at 5.51, 6.10, 7.55, 8.87, 9.52, and 9.91 Mev. The levels at 5.51 and 6.10 Mev have not previously been detected.