Dielectric and piezoelectric responses of slightly textured, lead barium niobate ceramics are studied. The designed morphotropic phase boundary composition (Pb0.63Ba0.37Nb2O6) shows considerable nonlinear dielectric and piezoelectric responses. While these nonlinear behaviors lead to significant instabilities of the functional properties, interesting features are revealed as a consequence of the texturing effect in the composition studied. An improved dielectric performance and a lower nonlinear piezoelectric response are observed when the electric field is applied to the sample in the forging direction. The results are quantitatively discussed in the framework of the Preisach and Rayleigh models. In this context, a decrease in the nonlinear response can be associated with a lower grain size related to the texture. The results of this work show that texturing is an effective route for controlling the undesirable nonlinear behavior of piezoceramics with tetragonal tungsten bronze structure.