Give the contract to a lawyer. Before you consider the commercial elements of the contract, have a specialist music lawyer highlight any dangerous clauses. Terms such as "in perpetuity" may seem innocuous, but their inclusion in a contract can be the difference between your artists getting paid a fair amount or not. After the lawyer has examined the legalese and drawn up a redraft, return the contract to the third party.
Study the deal memo and make a list of initial changes. When a recording, publishing or performance contract is offered to an artist it is typically issued with a deal memo. It summarizes the commercial elements of the proposed contract, such as term, revenue share and obligations. The first contract is rarely the one that both parties agree on. Typically the artist and the party offering the contract meet somewhere in the middle. Consult with the artist and make a list of changes, starting with the most important. For example, if there is a clause that obliges the artist to work with any artist that the third party chooses, advise the artist to reject the offer and move to have that clause omitted.
Make a list of possible concessions. Discuss with your artist which items they are prepared to negotiate in favor of the other party. Bargaining power is crucial in contract negotiations. Some items in the contract may be less important to your artist than others. But the other person doesn't know this. For example, if the artist likes the work of an unknown, and therefore cheaper, video director, write "artist is willing to agree to a lower financial commitment to video." Use this concession to trade off against other more important elements, such as contract term.
Write to the third party's representative summarizing the artist's wishes. Don't include the potential concessions; keep these for later. The letter must first list the clauses that are unacceptable to the artist. Then include clauses that the artist would prefer not to agree to. It's important to be assertive, but don't use language that alienates the third party.
Present the third party response to the band. When the label, publisher or agent submits a new offer, read it with the artist and explain the commercial impact of the new draft.