Image Searches and Keywords

Question about how search engines associate keywords with image searches.

[WilliamWar]

At least some of the visitors to several of my websites appear to arrive there through searching through images (pictures from my site indexed by search engines). Google's image search for example.

What is the best way to use keywords to get more traffic through image searches?

Should my image "filenames" try to use keywords, like "widget.jpg" for somebody searching for widgets?

Or, do search engines tend to index the words before the image on the page, or do they tend to index the words immediately after the image?

How to optimize my page for image searches is essentially my question. Any thoughts?

[troels nybo nielsen]

In my own searches I see lots of images that do not have the search terms in file names or alt tags but only somewhere in the main text, so main text does count.

From my experiences a page should be optimised for an image title pretty much the same way as you optimise it for a keyword:

Page title tag: Green widgets.
Page file name: green-widgets.html
H1: Green widgets.
Image file name: green-widgets.jpg
Image alt tag: Green widgets.

And green widgets mentioned in text near top and near image.