Current methods in qualitative physic sometimes predict behaviors of physical systems that do not correspond to any realvalued solution. One reason is that the merging of distinct behaviors cannot be avoided by local criteria. It is necessary to determine the possible continuations of a qualitative behavior taking into account its complete history. Such global criteria for the partial elimination of spurious solutions are developed for 2nd order differential equations. The application of these filters is shown to reduce the set of behaviors for the mass-spring system predicted by other qualitative physics systems.