The idea of rearranging generation assets amongst firms to improve competition has once again surfaced in a recent report on improvements to the New Zealand Electricity Market. We present counterexamples to show that rearranging assets, either with asset divestiture to a new firm, or asset swaps between existing firms, may actually reduce competition in electricity markets. Our examples emphasize features that are particular to electricity, such as seasonality and transmission constraints. These results warn that applying economic rules of thumb to electricity markets may lead to erroneous conclusions.