When developing models of biochemical reaction networks, we typically run into two problems: the network itself is somewhat uncertain, and many of the kinetic constants are unknown. Most biochemical modelling therefore involves the generation and testing of hypotheses in the presence of incomplete data. Often, the models are more elaborate than can be entirely justified by the data, but it is less than clear where models can be pruned. Qualitative stability analysis methods, often associated with graphical analyses, provide necessary conditions for models to have specified behaviours, such as oscillations or multistability. Accordingly, they can both identify the generator of a particular behaviour in a model and suggest what parts of the model are superfluous. Following a brief review of Ivanova's qualitative instability theorems, some theorems for model reduction based on this theory will be outlined and illustrated.