To be honest we normally operate under the assumption that the council will refuse everything you say, and you'll only get a fair hearing at the tribunal anyway, at which point the full sum is in play.
Frankly the discount is just a distraction, the only way to guarantee that you can settle at the discounted rate is not to challenge the PCN at all and just pay it as soon as you get it. Challenging a PCN and then paying when the challenge is rejected by the council is the worst option, as you've spent time fighting the penalty and you have absolutely nothing to show for it.