What if the feds targeted inflation rate were lower?

I've often read that the Federal Reserve controls the money supply with a goal of having the inflation rate be around 2%. I'm wondering if there would be benefits in having the targeted completion rate be much closer to zero. Over the long term, 2% is a lot. Why wouldn't 0% be desirable for the long-term planning we expect from businesses and other organizations? I understand that deflation is bad. But I'm not advocating any extended period of deflation. I'm just saying that if I ran the Fed, I would want to have a month or two with the inflation rate slightly below zero, followed by a month or two with the inflation rate selling above zero, such that it averages to 0%. What do you think?