How to recover data encrypted by CryptoDefense ransomware

With sophisticated ransomware you generally have only two options: pay the ransom or reformat and backup. The former is a contentious issue, with some security experts recommending paying up and trusting the criminals not to abuse your credit card data and to provide you with a working key. I am not in that camp, and wonder why I would trust someone who has already blackmailed me into paying a fee like this and who obviously doesn't care if I get my data back or not? The second option isn't always much better either as it relies upon many variables, including whether your backup data has been infected/encrypted, whether your PC is accessible enough to perform a full reformat and start again, and so on. In the case of CryptoDefense there is a third way, for a lucky (or should I say unlucky) few whose computers were infected before April 1st, 2014.