I think the answer depends on how many schools you like, and what's your confidence level about getting admitted. If you are determined to go private, then definitely have at least 1-2 safety schools on your list. Here are the results (
https://spreadsheets.google.com/viewanalytics?formkey=dFFHRklQWDFuOWNaSlMtdlRPd3hORmc6MA) of a rough admissions survey I set up last year (
http://www.dcurbanmom.com/jforum/posts/list/151144.page). It looks like most people apply to at least 3-4. I believe the high number of people applying to only one school are most likely younger siblings of already admitted students.