This paper identifies computationally the microstructural textures that would reduce anisotropy in elastic and plastic properties of titanium alloys, including Ti–6Al–4V, CP-Ti, and Ti–7Al. The approach employed is a new data-driven optimization method that combines two kinds of modeling techniques: combinatorial optimization and 3D crystal plasticity constitutive model. We show that the designed textures can minimize anisotropy, while maximizing either stiffness or strength, an achievement not possible with any experimentally reported texture to date. The designed textures consist of several highly oriented textures, as few as five orientations, contradicting the belief that these textures need to be uniformly random.