Still, it makes the site unnecessarily slow. After some investigation, I found out that it looks like Wordpress uses 32MB of memory by default - and that's really not much.
Editing your wp-config.php file, you can add the line:
to increase the limit. I decided on 96MB for a start, but maybe 64MB will be enough for you - I'll leave that to you.
Anyway, now Wordpress scales images I upload correctly. It won't fix older images, but I can live with the big pictures in my archives.