Strain and nanoscale variations in composition can significantly alter the electronic and optical properties of self-assembled alloy quantum systems. Using a combination of finite element and first-principles methods, we have developed an efficient and accurate technique to study the influence of strain and composition on the quantum confinement behavior in alloy quantum dots. Interestingly, we find that a nonuniform distribution of alloy components can lead to an enhanced confinement potential that allows a large quantum dot to behave electronically in a manner similar to a much smaller dot. The approach presented here provides a general means to quantitatively predict the influence of strain and composition variations on the performance characteristics of various small-scale alloy systems.