For given acoustic frequencies of premixed gas-turbine combustors, a classical method not currently in use is explored for assessing whether acoustically driven oscillatory combustion will occur. The method involves cataloging linear amplification and attenuation mechanisms and estimating magnitudes of their rates. Linear approximations to nonlinear mechanisms are included in an effort to obtain a reasonably complete description. A stability index is defined such that oscillation is predicted to occur when the value of the index exceeds unity. The method is tested on the basis of new experiments and experimental data available in literature. Moderate success is achieved in rationalizing these experimental results. The objective of the method is to enable quick and inexpensive decisions to be made for a wide variety of potential design configurations and operating conditions, without the complexity of computational fluid dynamics. The approach therefore may complement other approaches already in use.