This paper focuses on directional texture analysis. We propose a new approach for orientation estimation. This ap-proach hinges on two classes of convolution masks, i.e. the gradient and the valleyness operators. We provide a framework for their optimization regarding bias reduction and noise robustness. As the gradient and the valleyness operators are complementary, we propose a combination named GV-JOE. This combination consists in using the gradient on inflexion pixels, the valleyness on crests and valleys, and a linear mix-ture of both of them elsewhere. We implement an adaptive selection of the size of our operators, in order to take into account the variations of the texture scale in the image. We exercise our approach both on synthetic and natural textures. These experiments show that, when used sepa-rately, both classes of operators are more accurate than classical derivative approaches. In noisy cases, the GV-JOE implementation improves the robustness of our operators without affecting their accuracy. Moreover, compared to well known orientation estimators, it gives the best estimates in the most difficult cases i.e. for high frequency textures and low SNR.