The C-12(C-12,O-14) two-proton pick-up reaction has been measured at 211.4 MeV incident energy to study the structure of states of Be-10 up to excitation energies of 12 MeV. The measured partial angular distributions show pronounced oscillatory shapes, which were described by coupled-reaction-channels calculations. Spin-parity assignments could be derived from these characteristic shapes and two definite assignments have been made. The state at 11.8 MeV has been identified as the 4(+) member of the ground-state band, and the state at 10.55 MeV is assigned J(pi)=3(-). At 5.96 MeV only the 1(1)(-) member of the known 2(2)(+)/1(1)(-) doublet is populated. The angular distribution of the peak at 9.50 MeV, which consists of several unresolved states, has been unfolded using contributions from known states at 9.56 MeV, 2(+), and 9.27 MeV, 4(-). The inclusion of a state at 9.4 MeV reported by Daito from the B-10(t,He-3)Be-10 reaction and tentatively assigned (3(+)) improved the fit considerably. A K=2 band is formed with the 2(2)(+) state as the band head and the (3(+)) state as the second member. The structures of the K-pi=0(1)(+),2(2)(+), and 1(1)(-) bands are discussed.