This paper presents a novel power flow method suitable for radial distribution feeders, which consists a modification of the simplified power flow concept known as the DistFlow method, already available in the literature. The proposed method relies upon a differentiated manipulation of power losses, which are taken into account in voltage calculations, unlike other simplified methods, where losses are totally neglected. As a result, calculation accuracy is greatly improved, in terms of node voltages, losses and overall active & reactive power flows. In addition, the proposed method is non-iterative and entirely linear, being easily implementable and fast in execution. The method is particularly suited for feeders with a high penetration of Distributed Energy Resources (DER), providing results that closely match those of a full non-linear power flow and are considerably more accurate than the traditional linearized distribution power flow methods, without any increase in computational burden. The new method is applied to a variety of case studies in the paper, to demonstrate its accuracy and effectiveness, comparing its performance with the simplified (linearized) DistFlow and a conventional non-linear power flow method.