In a recent work, Doerr and Fouz [\emph{Asymptotically Optimal Randomized Rumor Spreading}, in ArXiv] present a new quasi-random PUSH algorithm for the rumor spreading problem (also known as gossip spreading or message propagation problem). Their \emph{hybrid protocol} outperforms all known PUSH protocols. In this work, we add to the hybrid protocol a direction-reversing element. We show that this \emph{direction-reversing quasi-random rumor spreading protocol with random restarts} yields a constant factor improvement over the hybrid model, if we allow the same dose of randomness. Put differently, our protocol achieves the same broadcasting time as the hybrid model by employing only (roughly) half the number of random choices.