This letter proposes a novel one-layer coding/shaping scheme with single-level codes and sigma-mapping for the bandwidth-limited regime. Specifically, we consider non-uniform memoryless sources sent over AWGN channels. At the transmitter, binary data are encoded by a Turbo code composed of two identical RSC (Recursive Systematic Convolutional) encoders. The encoded bits are randomly interleaved and modulated before entering the sigma-mapper. The modulation employed in this system follows the unequal energy allocation scheme first introduced in . The receiver consists of an iterative demapping/decoding algorithm, which incorporates the a priori probabilities of the source symbols. To the authors' knowledge, work in this area has only been done for the power-limited regime. In particular, the authors in  proposed a scheme based on a Turbo code with RSC encoders and unequal energy allocation. Therefore, it is reasonable to compare the performance - with respect to the Shannon limit - of our proposed bandwidth-limited regime scheme with this former power-limited regime scheme. Simulation results show that our performance is as good or slightly better than that of the system in .