Understanding screech is especially important for the design of advanced aircraft because screech can cause sonic fatigue failure of aircraft structures. Although the connection between shock-cell spacing and screech frequency is well understood, the relation between non-uniformities in the shock-cell structures and the resulting amplitude, mode, and steadiness of screech have remained unexplored. This paper addresses the above issues by intentionally producing spanwise (larger nozzle dimension) variations in the shock-cell structures and studying the resulting spanwise screech mode. The spanwise-oblique shock-cell structures were produced using imperfectly expanded convergent-divergent rectangular nozzles (aspect ratio = 5) with non-uniform exit geometries. Three geometries were studied: (a) a nozzle with a spanwise uniform edge, (b) a nozzle with a spanwise oblique (single-bevelled) edge, and (c) a nozzle that had two spanwise oblique (double-bevelled) cuts to form an arrowhead-shaped nozzle. For all nozzles considered, the screech mode was antisymmetric in the transverse (smaller nozzle dimension) direction allowing focus on changes in the spanwise direction. Three types of spanwise modes were observed: symmetric (I), antisymmetric (II), and oblique (III), The following significant results emerged: (i) for all cases the screech mode corresponds with the spanwise shock-cell structure, (ii) when multiple screech modes are present, the technique presented here makes it possible to distinguish between coexisting and mutually exclusive modes, (iii) the strength of shocks 3 and 4 influences the screech source amplitude and determines whether screech is unsteady. The results presented here offer hope for a better understanding of screech and for tailoring shock-containing jets to minimize fatigue failure of aircraft components.