Conversation so far:
When did Tom Petty join the Traveling Wilburys?
In 1988, Tom Petty joined George Harrison's group, the Traveling Wilburys.
What did Tom Petty do in the Traveling Wilburys?
For the Traveling Wilburys' Traveling Wilburys Vol. 3. album, Bob Dylan and Tom Petty became lead vocalists as George Harrison ceded the role to them.
Who else was in the Traveling Wilburys besides Tom Petty, George Harrison, and Bob Dylan?
Besides Tom Petty, the Traveling Wilburys featured Bob Dylan, George Harrison, Jeff Lynne and Roy Orbison.
Was there any tension within the Traveling Wilburys?
Tom Petty recalled that the band members of the Traveling Wilburys wanted to clear the air with Bob Dylan and not be  deferential to him.
Are there any other interesting aspects about the Traveling Wilburys besides when Tom Petty joined, what Tom Petty did for the band, who was in the band, and if there was tension within the band?
Traveling Wilburys members adopted tongue-in-cheek pseudonyms as half-brothers from a fictional Wilbury family of travelling musicians.
Why did Petty leave the Traveling Wilburys?
Tom Petty left the Traveling Wilburys in 1991 after George Harrison was unenthusiastic about touring and continuing the project.

Question: What was the new songs for?
Self-contained rewrite: What was the Traveling Wilburys' new songs for?