To cope with the explosive traffic growth of next-generation wireless communications, it is necessary to design next-generation multiple access techniques that can provide higher spectral efficiency as well as larger-scale connectivity. As a promising candidate, power-domain non-orthogonal multiple access (NOMA) has been widely studied. In conventional power-domain NOMA, multiple users are multiplexed in the same time and frequency band by different preset power levels, which, however, may limit the spectral efficiency under practical finite alphabet inputs. Inspired by the concept of spatial modulation, we propose to solve this problem by encoding extra information bits into the power levels, and exploit different signal constellations to help the receiver distinguish between them. To convey this idea, termed power selection (PS)-NOMA, clearly, we consider a simple downlink two-user NOMA system with finite input constellations. Assuming maximum-likelihood detection, we derive closed-form approximate bit error ratio (BER) expressions for both users. The achievable rates of both users are also derived in closed form. Simulation results verify the analysis and show that the proposed PS-NOMA outperforms conventional NOMA in terms of BER and achievable rate.