Need help copying directories

I would like to make a copy of directory on a second hard drive. I want all of the links resolved and the actual files copied, even if I end up with duplicates under different subdirectories on the target media. I tried -- cp -R source dest but there are still links in dest. I don't see any options under man for cp that says to do what I'm trying to do. Will cp do this? If not, what other command can I use? Thanks, Greg Wallace