as days pass by

I run into this problem a lot. Imagine I’ve got a picture of, say, Sam and I at a party. I’d like to post that picture here. So, I’d have the picture and then, below it, a caption saying “This is Sam and I at the Beckham’s party“. But then what should I use as the alt text on the picture? Clearly the alt text should be “Sam and I at the Beckham’s party“, or perhaps even a longer description of the image. However, then the caption is redundant; if someone browses the page with images off then it will (correctly) display the alt text in place of the picture, leaving the page saying “This is Sam and I at the Beckham’s party. Sam and I at the Beckham’s party.”
Those of you saying: appropriate alt text for that image is therefore the empty string, since there already is a caption in the HTML; what should I do if i want the image to be a link to beckhams-party.com? If I make the alt text empty then the link is unusable in text-only browsers.
Perhaps I should, for example, make the alt text empty and wrap both the image and the caption in the link, thus covering both those bases. That only works if the caption is the thing immediately following the image, though. Semantic HTML people, what would you recommend?