Over a period of several years we have performed three separate experiments at Lawrence Berkeley National Laboratory's 88-Inch Cyclotron in which 235 U (thick target) was Coulomb-excited. The program involved standalone experiments with Gammmasphere and with the 8pi Spectrometer using 136 Xe beams at 720 MeV, and a CHICO-Gammasphere experiment with a 40 Ca beam at 184 MeV. In addition to extending the known negativeparity bands to high spin, we have assigned levels in some seven positive-parity bands which are in some cases (e.g., [631]1/2, [624]7/2, and [622]5/2) strongly populated by E3 excitation. The CHICO data have been analyzed to extract E2 and E3 matrix elements from the observed yields. Additionally, many M1 matrix elements could be extracted from the γ-ray branching ratios. A number of new features have emerged, including the unexpected attenuation of magnetic transitions between states of the same Nilsson multiplet, the breakdown of Coriolis staggering at high spin, and the effect of E3 collectivity on Coriolis interactions.