ANA miles can be converted to ANA shopping points on a 1:1 basis (1 mile : 1.2 points until end Jan.31). These points can be used at ANA's shopping site www.astyle.jp , with each point being equivalent to 1 yen.
There are a lot of items that can be bought for less than 6,000 points (6,000 yen).

The site's all in Japanese however, and items can only be delivered to a Japanese address...

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Whoops sorry, this option also needs a minimum of 10,000 miles