We present the results of an analytical study concerned with the frequency resolution of our adaptive additive synthesis model. First, we derive the relation between the characteristics of the piece wise polynomial parameter trajectories of the model and the frequency resolution that can be obtained by means of adapting the model using a minimum error objective. Second, we present an analytical investigation of the problem to model signal resonances beyond the frequency resolution of the model. Based on the analytical description of the situation a new solution is proposed that leads to high quality additive models of non stationary sounds with dense resonances, i.e. choir or drum sounds, and provides increased robustness with respect to sound transformations.