'Save Site As Template' permissions

Hello -

I granted a user full control/design permissions on a susbite.   He is unable to see the 'Save site as template' option.   Publishing features are turned off on the site, but enabled on the parent site.   Do I need to turn it off at the parent level too?  I didn't think that was the case.

Also, what permissions are required to save the template to the solutions gallery (_catalogs/solutions/Forms/AllItems.aspx)?    I had a user with full control to that library try and he got an access denied error.

thanks