We propose a new transmission scheme, which we call Decode-Partial-Forward (DPF), for orthogonal half-duplex relay channels. We demonstrate that the DPF scheme achieves significantly higher rates than the conventional DF scheme that is based on repetition coding and it performs close to the capacity bounds of DF relaying. In DPF, the source superimposes two separate codewords and the relay decodes both codewords but it regenerates (forwards) "the more difficult to decode" codeword only. The destination node applies successive interference cancellation in order to decode the two codewords based on the received signals in both time slots. We provide a closed-form solution to find the optimal power and rate allocation for the two superimposed codewords in order to maximize the sum achievable rate. The DPF scheme provides a simple and practical alternative to the advanced cooperative coding techniques.