When we upgraded our server a year and a half ago, we also upgraded our
Tivoli from ADSM Ver. 3.1X  to TSM Ver. 3.7X
The method we chose was:
1. Performed a fresh install of Ver. 3.7 to the new server from the CD, and 
applied the latest PTF.
2. Set up database volumes, log volumes, defined the storage pools, etc.
3. Made sure that everything was working OK on the new server.
4. Upgraded ADSM on the old server to the same level TSM as the new server.
5. Ran the upgraded server for a few days without any problems.
6. Backed up the database on the old server, and restored the database to the 
new server.