A spectrum-sharing scenario in a cognitive radio (CR) network where a secondary user (SU) shares a narrowband channel with N primary users (PUs) is considered. We investigate the SU ergodic capacity maximization problem under an average transmit power constraint on the SU and N individual peak interference power constraints at each primary-user receiver (PU-Rx) with various forms of imperfect channel-state information (CSI) available at the secondary-user transmitter (SU-Tx). For easy exposition, we first look at the case when the SU-Tx can obtain perfect knowledge of the CSI from the SU-Tx to the secondary-user receiver link, which is denoted as g 1 , but can only access quantized CSI of the SU-Tx to PU-Rx links, which is denoted as g oi , i = 1,..., N, through a limited-feed back link of B = log 2 L b. For this scenario, a locally optimum quantized power allocation (codebook) is obtained with quantized g 0i , i = 1,..., N information by using the Karush-Kuhn-Tucker (KKT) necessary optimality conditions to numerically solve the nonconvex SU capacity maximization problem. We derive asymptotic approximations for the SU ergodic capacity performance for the case when the number of feedback bits grows large (B → ∞) and/or there is a large number of PUs (N → ∞) that operate. For the interference-limited regime, where the average transmit power constraint is inactive, an alternative locally optimum scheme, called the quantized-rate allocation strategy, based on the quantized-ratio g 1 /max i g oi information, is proposed. Subsequently, we relax the strong assumption of full-CSI knowledge of g 1 at the SU-Tx to imperfect g 1 knowledge that is also available at the SU-Tx. Depending on the way the SU-Tx obtains the g 1 information, the following two different suboptimal quantized power codebooks are derived for the SU ergodic capacity maximization problem: 1) the power codebook with noisy g 1 estimates and quantized g oi , i = 1,..., N knowledge and 2) another power codebook with both quantized g 1 and g oi , i = 1,... , N information. We emphasize the fact that, although the proposed algorithms result in locally optimum or strictly suboptimal solutions, numerical results demonstrate that they are extremely efficient. The efficacy of the proposed asymptotic approximations is also illustrated through numerical simulation results.