This paper develops a formalism for optimizing nozzle location/configuration with respect to combustion stability of high-frequency transverse modes in a can combustor. The stability of these acoustically non-compact flames was assessed using the Rayleigh Integral (RI). Several key control parameters influence RI – flame angle, swirling strength, nozzle location, as well as nozzle location with respect to the acoustic mode shape. In this study, we consider a N-around-1 configuration such as typically used in a multi-nozzle can system and study the overall stability of this system for different natural transverse modes. Typically, such nozzles are distributed in a uniformly circular manner for which we study the overall RI and for cases where RI > 0, we optimize the nozzle distribution that can reduce and minimize RI. For a fixed geometry such a circular configuration, the analysis shows how the flame’s parameters must vary across the different nozzles, to result in a relatively stable system. Additionally, for a fixed set of flame parameters, the analysis also indicates the non-circular distribution of the N nozzles that minimizes RI. Overall, the analysis aims to provide insights on designing nozzle locations around the center nozzle for minimal amplification of a given transverse mode.