I just switched to WordPress 1.5. Update went very smoothly. Thanks to the ssh access to this site, I could very easily backup and mirror it to my home Linux box. Here I duplicated the directory tree another time into a directory named wordpress, keeping additional copies of index.php, wp-config.php and wp-layout.css. Then I simply untared the WordPress distribution over the directory. After putting index.php and wp-layout.css into the theme directory, editing it according to upgrade instructions and editing database userid and password into wp-config.php I was basically all set. After invoking upgrade.php the new version was operable on my home box.
Only thing I then needed to do is to resync the directory tree back to the web site and invoke upgrade.php. That was all.
The plugins authimage and iimage-browser need to be updated as well, but this will have to wait until this evening.