I have heard that there is a substitute for eaves troughs called a water deflector which is angled out at 45 degrees protruding approx. 2" out past the singles. Is this true? Web site?
If you are not worried about water at ground level of your house they would probably work OK. What they do is create a spray out of the water coming off the roof and drop water on the ground. In areas where water runoff is a problem they don't work.