Don't know who downvoted you but I absolutely agree. I have a few homes that I help rent with and having a good tenant is high above and away better than having a bad tenant pay more money. Just the cost alone in time is worth giving a good tenant cheaper rent.
I think the normal reasoning is that higher rent filters out the bad tenants (statistically). But once you have a good tenant then you probably don't want to raise the rent unless they move out and you're seeking a new one.
Another way to screen out bad tenants is to offer zero deposit for high credit score applicants. Several large apartment buildings in my city (DC) do this, and the buildings are full of professionals.
It is totally legal to refuse to rent to people with low credit scores, so that's an option too. Just keep the standard consistent no matter who your applicant is and have a standard criteria to keep everything both fair and legal.
You probably can also charge a larger than average security deposit to weed out the people with cashflow problems. Most states have a cap on amount of security deposit collected, I know here it is twice the monthly rent if under 60. Otherwise the cap is one month's rent.
Here's the rub: You usually gotta have a great place to rent that attract such tenants.
DISCLAIMER: I am not a landlord but I am considering becoming one. Yes, I FULLY know the risks, my parents were landlords for over a decade. So I know exactly what NOT to do as they only made pennies. My grandparents are also landlords and make plenty of money on their rental properties, so I have a positive model as well as a negative one. :)
You probably know this, but for the sake of anyone else reading, your home state probably offers a brochure on how to be a landlord, including what rights you must enforce. It's essential if you ever get a bad tenant. Plus, find a real estate lawyer to go over your lease and whom you can go to in trouble comes up.