This paper considers the sum-rate (SR) maximization problem in downlink multi-user multiple input simgle output (MU-MISO) systems under imperfect channel state information at the transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This rate-splitting (RS) approach was shown to boost the achievable degrees of freedom when CSIT errors decay with increased SNR. In this paper, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of sample average approximation coupled with the weighted minimum mean square error approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared with conventional transmission with no rate-splitting.