How in-depth do your songs need to be before you meet with a producer to go over them?
A producer's job isn't to babysit your songwriting process. A producer's job is to produce a good recording, which is why a producer is called a producer. You should have the whole thing written, practiced, and ready to record before you enter the studio.
Agreed with Cavalcade. There are times when a producer does contribute in the songwriting process, but this is usually after he or she has worked with an artist/group before and has been "brought into the fold" so to speak, beyond merely directing the recording process; or the artist/group has a well-established sound that the producer can guide songwriting/arranging ideas towards. And these groups generally already have a mountain of material that the producer is merely helping to hone into the best possible songs for the best possible album.
"When you do something right, it seems as if you've done nothing at all."
Yeah, like the other guys said it should be 100% complete in your opinion, but remember to keep an open mind for accepting suggestions of improvement.
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