Shipment returned undelivered

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I have just had a customer enquire where their order was as they ordered it approx 3 weeks ago. I shipped this item from the UK to the USA via Royal Mail 'international signed for' cost of shipping was £10.60, the value of the product was only slightly more.


I have used the tracking feature on the USPS website which tells me: 
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"Your item was returned to the sender on June 13, 2003 because the addressee was not known.

Here is what happened earlier:
a.. NOTICE LEFT, June 12, 2003, 8:39 am, ODEN, MI 49764
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I print my packing slips directly from within osC so the address for shipping is exactly as the customer entered.

I think that I should refund the customer for the product, but not for shipping as it can hardly be our fault if he has addressed incorrectly or is not available to receive his order.

I really do want to build up a good reputation for Customer service as we are in a very competitive field, but at the same time we cannot afford to lose money due to customer errors, if that's what it is....

How do you guys handle this situation?