I base my payment structure on 33% deposit, 33% on concept approval and a final 34% on completion of the project.

This way I get paid for all the initial work I do for clients if they decide to cancel the project at any stage. I also refund portions of deposits if I have not completed sufficient work to warant keeping the whole deposit.

Now, the simple way to let clients know you won't work without a deposit is to say something like this:

"The payment structure is as follows: 33% deposit, this is required before I begin work and must accompany a signed contract; 33% payment when you approve a concept and a final 34% at project completion"

If clients do not like the idea of paying a deposit let them know it is fully refundable, if the project is cancelled, and no work has been done up to the date of cancellation. Let them know that this is simply your payment structure and protects you for work done. Ask them if they would be prepared to put 5 - 6 hours into needs analysis meetings/research and building their quote for free, then come up with several concepts for presentation for free (possibly taking 2 - 3 weeks, or more)?

It is not a matter of persuading your client, it is a matter of explaining to your client the professional requirements of dealing with you.