It sounds to me as though most of the content from old site is staying but that 3 enigmatic 'tools' are being moved to a new domain.
In which case I would want to be sure that the functionality being moved wasn't the cause of the previously lifted penalty, especially from a Panda perspective (given that the tools on the new domain presumably won't have any links pointing to it, Penguin shouldn't be an issue) - as a penalty would be re-applied if the tools are not Panda-friendly.
So:
- if you want to have the tools on both sites, I'm with Pete - noindex the tools on the old site.
- if you are permanently moving the tools, review them for Panda-friendliness and then noindex the old site's URLs, probably worth blocking the old URL in robots.txt as well.
- If your previous penalty was nothing to do with the tools at all, and the link profile of those pages is good (or if there aren't any links) then 301 the old URLs to the new.
That's if between Pete and myself we've understood correctly what you're trying to achieve.
Good Luck!