Using Migration Assistant

Hi. I just used Migration Assistant for the first time to transfer all my files from a Time Machine backup of my old MacBook Pro to a newer iMac via Firewire 800. Before I initiated the transfer I created a user account on the new computer with a new name and also a home folder with a new name. All the files appear to have been transferred but there is a problem.

My old home folder with all its contents from the Time Machine backup was copied to my new Users folder as a normal folder. Also in my new Users folder is my new home folder which has the little house icon and its own collection of Desktop, Documents, etc. folders (I first realized something was not right when my new desktop remained totally clean with none of the folders, etc. showing up that used to be on my old desktop).

Do I just drag the contents from each of the folders in my old home folder (which is now a normal folder on the new computer) into the corresponding folders inside my new home folder or did something go wrong in the migration process? I'm particularly concerned about moving files from my old Users Library folder into the new one. At this point the new computer is running beautifully and all my applications are working except for one which I may have to re-install.

Both my old MacBook and the new imac are running OS X 10.6.8.