Using a simple example and simulations, we explore the impact of input tree shape upon a broad range of supertree methods. We find that input tree shape can affect how conflict is resolved by several supertree methods and that input tree shape effects may be substantial. Standard and irreversible matrix representation with parsimony (MRP), MinFlip, duplication-only Gene Tree Parsimony (GTP), and an implementation of the average consensus method have a tendency to resolve conflict in favor of relationships in unbalanced trees. Purvis MRP and the average dendrogram method appear to have an opposite tendency. Biases with respect to tree shape are correlated with objective functions that are based upon unusual asymmetric tree-to-tree distance or fit measures. Split, quartet, and triplet fit, most similar supertree, and MinCut methods (provided the latter are interpreted as Adams consensus-like supertrees) are not revealed to have any bias with respect to tree shape by our example, but whether this holds more generally is an open problem. Future development and evaluation of supertree methods should consider explicitly the undesirable biases and other properties that we highlight. In the meantime, use of a single, arbitrarily chosen supertree method is discouraged. Use of multiple methods and/or weighting schemes may allow practical assessment of the extent to which inferences from real data depend upon methodological biases with respect to input tree shape or size.