My wifes Kindle broke, I'd bought her a new case she wanted and unfortunately it didn't offer the same protection as her previous case and damaged the screen - the image was stuck on the screen, it had obviously been lent on.
We contacted amazon by the live chat and after explaining what had happened they offered her a rather large list of refurbished Kindles with further discounts then on the website - Kindle Fire was included but my wife has never been a fan of that one. She only had a 4th generation with buttons but that wasn't available from my memory it seemed there weren't any basic E-Ink versions - mainly Paper White and Kindle Fires - she was going to purchase a Paper White for 65 but when I saw that the 3g model was only £8 dearer, £73, I told her to get that one.
I know its only refurbished but it seemed like a steal to me.
Currently, Amazon website don't offer that model as refurbished only new, which is much more expensive - £169 - http://www.amazon.co.uk/gp/product/B00JG8GBDM/ref=fs_pnwf
The Kindle did take a bit longer to arrive than expected she ordered it Boxing day and it only arrived today but seems worth it.
Amazon have said we have to send the broken Kindle to them or they will charge us the difference. I guess it stops everyone claiming they've got a broken Kindle. To be fair, we never bought the Kindle new originally, we brought it second-hand from CEX - so it's win-win all round.
I guess if you were being sneaky purchasing a secondhand Kindle and exchanging that for a refurbished one through Amazon live-chat would still work out cheaper than purchasing it directly. Just a thought;)