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I think that you would have a lot of upset employees if you tried to make the change after allowing for BYOD. If you have never supported BYOD, then the idea might well be a popular one. "Hey, our company is so cool they are giving us all an iPhone 4S." It's much easier to be seen as giving people something versus taking something away. Either way, if IT is spending so much time on supporting "unsupported" devices that it is preventing work that is actually productive from being done in a reasonable timeframe, I would suggest presenting the issue to whoever is charge of hiring as the cost of additional hires vs. providing devices.