What If the Agent says No Unsolicited Material?

My mother was keen that I was well brought up, and therefore the idea of sending out my work to someone who said No Unsolicited Material was completely unthinkable. I took it at face value. However, then I went to a talk given by an agent who worked for an agency that said they didn't look at unsolicited material. Someone in the audience stuck their hand up and asked about it.

'Oh, that,' the agent said blithely. 'We put that on to deter the no-hopers. We reckon anyone with the nerve to send out despite the notice is probably more determined than other writers, and we want to work with very determined writers.'

Now, personally I'd have thought it would mean that either people were determined or it was proof they didn't do their homework, but I'm not an agent. I've heard it since reiterated by other agents and editors. They may say they won't look at unsolicited material but they can't resist looking at it if it comes in - the biggest fear in publishing is that you'll be for ever remembered as the person who turned down the next JK Rowling/John Grisham/Stephen King...

So if you're certain that an agent is who you'd like to represent you, I'd disregard any comments in the Writers and Artists' Yearbook/The Writer's Handbook that they don't look at unsolicited material. Write to them, making it clear why you've chosen that particular agent. And if it gets returned by the next mail, obviously unlooked at? What have you lost apart from some postage?