When investigating combustion instabilities using analytical models, it has previously been assumed that the compact flame assumption implied that the flame-front movement did not need to be taken into account to solve the acoustics. This article shows that this is not necessarily the case. This article presents a generalization of such models of anchored V-flames to allow the flame "source" of acoustic waves to vary its position in time so as to track the flame-front location. A method for solving this problem is then presented. It is found that accounting for the flame front movement can alter both the linear stability of the combustor, and (for cases that remain unstable) the limit cycle amplitude. Significant changes in limit cycle amplitude are observed across a large range of operating conditions. The flame front movement has so far only been seen to provide a stabilizing effect, reducing the Rayleigh source term. Self-tuning regulator adaptive control methods appear to be unaffected by accounting for the moving flame front.