The ground-state band of 159Tb has been Coulomb excited up to spin 23/2 by 151-MeV 4~ions. The lifetimes of the 9/2 to 23/2 levels have been determined by combining results obtained with the RD and DSA methods, the E2/M1 mixing ratios for AI=I transitions have been measured using angular correlation techniques and the branching ratios for the levels up to spin 17/2 have been determined. The energies of the levels and the reduced M1 and E2 transition probabilities for their decay have been compared with the predictions of the rotational model, without and with AK= 1 admixtures. No satisfactory agreement could be achieved for all available experimental data simultaneously.