In this paper, we analyze the capacity gains of opportunistic spectrum-sharing channels in fading environments with imperfect channel information. In particular, we consider that a secondary user may access the spectrum allocated to a primary user as long as the interference power, inflicted at the primary's receiver as an effect of the transmission of the secondary user, remains below predefined power limits, average or peak, and investigate the capacity gains offered by this spectrum-sharing approach when only partial channel information of the link between the secondary's transmitter and primary's receiver is available to the secondary user. Considering average received-power constraint, we derive the ergodic and outage capacities along with their optimum power allocation policies for Rayleigh flat-fading channels, and provide closed-form expressions for these capacity metrics. We further assume that the interference power inflicted on the primary's receiver should remain below a peak threshold. Introducing the concept of interference-outage, we derive lower bounds on the ergodic and outage capacities of the channel. In addition, we obtain closed-form expressions for the expenditure-power required at the secondary transmitter to achieve the above-mentioned capacity metrics. Numerical simulations are conducted to corroborate our theoretical results.