A search for high-spin states in 288i has been performed by n-7 coincidence measurements in the 25Mg(e, nT) reaction at E~= 14 and i5.5 MeV. Spin-parity assignments of the observed levels were obtained from n-7 angular correlation and lifetime measurements at E~= 14.5MeV. The ?,-decay of the 9,t64keV level was investigated separately with the 27Al(p,?,) reaction at the Ep=2,160 and 2,312keV resonances. Rotational bands with K~=3 -(comprising levels at E~=6,879, 8,413, 10,188 and 12,204keV), K ~ = 5-(comprising levels at E~ =9,702, 11,577 and 13,741 keV) and K ~ =0 + (comprising levels at E~=6,691, 7,381, 9,164 and ll,509keV) were observed. The finding of the latter band supports the idea of coexisting oblate and protate shapes in zsSi. A level at 14,643keV excitation energy has the properties of the I~=8 + member of the ground state band. There are additional positive-parity high-spin states which do not fit into rotational bands. All types of positive-parity states are well accounted for by shell model calculations.