I wouldn't close the aperture that far - you'll get other optical problems. I'd set it at F/11 at the smallest - you might not need that much.
When the aperture is wide open, think of the incoming rays as thick pencils of light, coming from all directions but being directed by the lens -- each "pencil" is brought to a point, forming a single spot on the sensor. When the aperture is wide open the pencils can only be sharpened at one tiny plane - the focused area. However, if the pencils were very thin, they would be pretty close to in-focus across a wider range. Therefore you narrow your aperture to restrict the thickness of incoming ray bundles(pencils)/which increase the depth of in-focus material, and then compensate for the darker image using longer shutter times (not higher ISOs).
Anonymous, I think the problem is exaggerated in your case because you have a very large, lovely camera sensor (IIRC - you have a Canon with an APS-C sized sensor, right?). The larger the sensor, the shallower the DoF for a given aperture/focal length. Compact cameras have less issues of this nature because both the sensor and aperture are tiny. DoF is something you can calculate easily - check out this calculator to get some idea of the numbers:
http://www.dofmaster.com/dofjs.html