Consider holding a "rental auction", looking for the prospective tenant who will and can pay the most rent or who can and will do the improvements you want.  

Question for those who've done this and tracked results:  Do you think I'll be better off sending to More houses, less times, like 600 prospects twice a year, or are results better to send to less people, more times, like 300 prospects four times a year?  

The prospective tenant has offered a pet deposit (it's illegal to require one in our jurisdiction).

What was the outcome?

That means your pool of prospective tenants will only get smaller if that trend continues, and there's no reason to think it won't.I hope I'm not discouraging you with my post. 

What was the outcome?

Then at that point, continue with another candidate.My pre-screening starts out with asking the prospective tenants to give me a copy of their Credit report and Score from one of the free credit reporting websites such as Credit Karma.

What was the outcome?

So if they are "month to month" then that might change the outcome if as compared to if they have 10 months remaining on the leases. 

I did not let one tenant keep a mastiff puppy that they snuck in then had to turn down a really great prospect with a tea cup poodle.