The nucleus Cd-108 has been studied using a heavy-ion reaction and the NORDBALL multi-detector array. The yrast band has been extended to I(pi) = 24+, and nine quasi-rotational side bands have been identified. The nuh11/2 negative-parity orbital is found to play a dominant role both in the low-spin as well as in the high-spin structure of Cd-108. The first band crossing in the yrast band is caused by the h11/2 neutrons. The 10+ state of the aligned nu(h11/2)2 configuration decays strongly into a low-lying low-spin intruder-like positive-parity band. It is suggested that this intruder structure is dominated by a non-aligned nu(h11/2)2 configuration. For the first time in this mass region, we report a collective, possibly prolate, Ml band built on the pi(g9/2)-2 configuration. The experimental results are discussed in terms of total-routhian-surface and cranked-shell-model calculations.