Qualitative simulation is a useful method for predicting the possible qualitatively distinct behaviors of an incompletely known mechanism described by a system of qualitative differential equations (QDEs). Under some circumstances, sparse information about the derivatives of variables can lead to intractable branching (or "chatter") representing uninteresting or even spurious distinctions among qualitative behaviors. The problem of chatter stands in the way of real applications such as qualitative simulation of models in the design or diagnosis of engineered systems. One solution to this problem is to exploit information about higherorder derivatives of the variables. We demonstrate automatic methods for identification of chattering variables, algebraic derivation of expressions for second-order derivatives, and evaluation and application of the sign of second- and third-order derivatives of variables, resulting in tractable simulation of important qualitative models. Caution is requir...