A frequent comment I hear when talking with musicians is that they think mailing a copy of their music to themselves will work just like a copyright registration, but cheaper. This is sometimes known as a “Poor Man’s copyright.” While this might (and I use the term loosely” be helpful from an evidence standpoint, it doesn’t really help with who created it and it will likely run into all kinds of evidentiary problems. Writers are much better off going ahead and filling out the copyright application. By filing a registration you set yourself up to collect attorney’s fees and potentially higher damages if you have to file a lawsuit. By the way, in order to even get into a court on a claim of copyright infringement you have to file a registration, but if you wait to long to register you may lose out on some forms of damages.
The better advice is to always put together a song writer split agreement – i.e. write what contribution (or percentage) of each song each person contributed. In a band setting it is good to have all members sign off, even if they did not contribute.
It is much easier to do things right the first time then to get into a fight over it later.