node-NAME.tpl.php doesn't override the node template. I've cleared theme registry I'm using Drupal 7.8, and I've tried the same thing I did with Drupal 6, making a custom layout for a node type.

I've copied node.tpl.php, and renamed it node-NAMEOFTHENODETYPE.tpl.php, altered the template, uploaded it to the theme folder.
Surprisingly, Drupal 7 doesn't take it: It shows the default node layout.

Can anyone tell me what I am doing wrong?
You mispelled the filename. Drupal 7 now uses double dashes (--); your file needs to be node--NAMEOFTHENODETYPE.tpl.php.