Great additional advice, two other thoughts building on it:
1) Make sure the client knows that you're doing work that's out of scope, but that you're not charging for. Otherwise they just think it's part of the package, and will expect it next time. I've seen consultants get upset that clients didn't appreciate all the extra work they were doing, when the clients didn't even know it was extra.
2) Stay firm on your rates, but offer discounts to clients for things that cost them nothing and help your business. Knock 10% off if they pay up front: it gives you cash in hand, saves you from having to follow up with accounts payable, and makes it harder for them to cancel the project. Offer a discount as part of a retainer or an ongoing support contract. Show them where there are opportunities for someone on their team to do the work, rather than engaging you. If you show them that you're a partner in helping them reduce costs, they'll value your services more.
Your second point is also a good way to deal with late payment penalties - something which it can be hard to add to a contract (as in, $x if you pay within 30 days $x + 10% if you're late).
Selling it as a discount for paying early is generally going to be easier to get a client to agree to - who doesn't like a discount? So it's $y normally, but $y - 10% if you pay within 30 days.
It's no effect on your bottom line, but it does make for happier clients!
The US also has usury laws, which I found fairly surprisingly when I was just starting out. I previously thought usury was a strictly a historic crime, like adultery or eating bacon on the sabbath. But some people are very much offended by the idea of lenders charging too high an interest rate.
They actually become relevant for late fees, since you usually do want your fee to be punitive enough to encourage timely payments. The usual practice is set your fee to 1.5% per month or the highest percent allowed by law (i.e. just below usury if that's applicable in your state).
1) Make sure the client knows that you're doing work that's out of scope, but that you're not charging for. Otherwise they just think it's part of the package, and will expect it next time. I've seen consultants get upset that clients didn't appreciate all the extra work they were doing, when the clients didn't even know it was extra.
2) Stay firm on your rates, but offer discounts to clients for things that cost them nothing and help your business. Knock 10% off if they pay up front: it gives you cash in hand, saves you from having to follow up with accounts payable, and makes it harder for them to cancel the project. Offer a discount as part of a retainer or an ongoing support contract. Show them where there are opportunities for someone on their team to do the work, rather than engaging you. If you show them that you're a partner in helping them reduce costs, they'll value your services more.