@Matthew Paul
I'm a contractor too and an appropriate deposit is fine but that is way less than 33%. Also, my post is written with a large project in mind, which might be our disconnect in deposit theory.
If you have sufficient credit at the supply houses; you are not a cash on delivery customer and probably get invoiced net 30 days after receiving an order. (without paying interest) Ergo, you are not financing the customers job anyways.
I'll give deposits on almost everything, but for 33% it'd have to be a pretty small project to warrant it. It just doesn't cost that much to show up for the first day. You can break up the progress payments small enough to solve almost any cash flow issue for the contractor (I pay my drywall crew daily) but until the material is on the property and/or installation is occurring, there isn't a need to pay premature invoices let alone writing a 33% check weeks before a job starts.
There are too many contractors that start asking for big deposits at the end of the month for me to feel comfortable prepaying for services in large amounts. Granted the state of CA is a little overbearing, but it's illegal to charge more than $1,000 as a deposit out here anyways. (Although most contractors aren't even aware of that law).
I think the only power the customer has in the payment schedule. The contractor gets to stop work and lien the property. The customer's only recourse after the money has been paid is to leave voicemails.