After starting to prescreen, the number of showings went down. However, before I prescrened as intensly as I do now I had a parade of home. One time there was a line out on the sidewalk when my DH showed up (LOL no joke). One thing I learned besides that I needed to screen better before showings is that having the showings close together is a very good thing. It shows the prospective tenants that they better move quickly if they are interested.
For me it was not that I was creating this senario, it just was. If I were renting a home that was not as bombarded with interest I would definatly mimic this senario.