Bivalve nacre is a brick-wall-patterned biocomposite of aragonite platelets surrounded by organic matter. SEM–electron back scatter diffraction analysis of nacre of the bivalve family Pteriidae reveals that early aragonite crystals grow with their c-axes oriented perpendicular to the growth surface but have their a- and b-axes disoriented. With the accumulation of successive lamellae, crystals progressively orient themselves with their b-axes mutually parallel and towards the growth direction. We propose that progressive orientation is a result of competition between nacre crystals at the growth front of lamellae, which favours selection of crystals whose fastest growth axis (b-axis) is oriented parallel to the direction of propagation of the lamella. A theoretical model has been developed, which simulates competition of rhombic plates at the lamellar growth front as well as epitaxial growth of crystals onto those of the preceding lamella. The model predicts that disordered nacre progressively produces bivalve-like oriented nacre. As growth fronts become diffuse (as is the common case in bivalves) it takes longer for nacre to become organized. Formation of microdomains of nacre platelets with different orientations is also reproduced. In conclusion, not only the organic matrix component, but also the mineral phase plays an active role in organizing the final microstructure.