Image URL's not working for me

I am using 3.5.2 and am trying to insert images into my text.

I'm developing on a local server (localhost), using Drupal7.0, and am using absolute urls
Because I'm developing on a local server for eventual deployment on the web I'm using urls like this:
"/images/map1.jpg"

I can insert the image, resize, etc. No issues in the editor.
But when I do a preview, or a view from another machine on the lan, the images are gone.
I repeated the edit on the lan-based machine and, hours of experimentation later, discovered the problem.

When an edit is performed on the local server, the image urls get changed and " http://localhost/ " is pre-pended to them.

So, naturally, if I view the images from my lan-connected machine they have disappeared.

Obviously I can avoid this problem from now on by only editing on my lan-connected machine, but it seems to be a bug in my eyes.
Yes or no? Thanks.