I don't know about Tasks, but for Calendar, this is possible.
Go into Versamail, and select Options -> Preferences -> AutoSync.
You'll see check boxes for Mail, Calendar, and Contacts. Select
what you want. If you don't select Mail, you won't be able
to do push, but you can set it to sync however often you
wish.
This is the configuration I use, using Exchange Active Sync in
Versamail to sync Calendar and Contacts, and, separately,
Chatteremail to do push email over IMAP.
- Saul |