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We show that Euclidean axion wormholes in theories of gravity coupled to asingle axion have several independent inhomogeneous perturbations that lowerthe Euclidean action. Our analysis relies on a judiciously chosengauge-invariant variable which makes the negative mode structure about axionwormholes transparent. Perturbations lowering the action are concentrated inthe neck region and exist for wormholes in flat space and in AdS. Theirpresence means axion wormholes are not relevant saddle points of the functionalintegral in quantum gravity. This resolves the paradoxes associated with thesesolutions from the viewpoint of AdS/CFT. We conjecture that the lower actionconfigurations one flows to are ensembles of microscopic `quantum wormholes'with unit charge.

Euclidean axion wormholes have multiple negative modes