The answer is that rather than giving up, market yourself to better customers.
Charge for a better service and deliver, and the clients who are a tier or two above the CraigsListers will use you. A guy that budgets $2500 for a 10k job was never going to be your customer no matter what you said.
Very sage advice right there
I have made a quite a few changes this year regarding these thoughts.
1) Free Estimates are only in writing if my gut feeling says to do so. Otherwise I'll give you a verbal ballpark.
2) I ask people what their budget is. If they don't want to share, they go to the bottom of my priority list
3) I do not advertise on Craigslist at all. I only use CL for buying or selling things. I don't hire from there (anymore) nor do I look for work from there.
4) I have a Facebook business page, but I don't troll all the groups looking for work. They aren't my customers and most likely won't be.
Recent example: I was working in a nearby town and a "potential" customer called looking for a price on a detached garage. I was in town so I stopped by to scope it out. Entire package was north of $17k. I shot him a price over the over phone. I got "geez, I was hoping this would be under $10k." After a quick laugh, I told him good luck with that. Permits, concrete, erosion control and materials were over $10k. Moral, the guy was nuts and will never be my customer. Just move on.
Another example: I got a call from a lady looking for a roof quote. She said I came "highly recommended from a Facebook group of her friends." She asked why I don't advertise there. I told her I can't compete with unemployed people, illegals, and side work jobbers. I gave her a price and got "We'll get back to you. We need more quotes". Really? WTF happened to highly recommended????
Point being, there are customers out there that WILL pay for quality, quick completion, premium materials, etc. They are just not easy to find. It is damn near impossible to find them if the first place you look is Craigslist and the second place you look is Facebook. Well, that's my experience anyway.