I would do it in portions over teh course of a couple of years if you are worried about having it come back. WHat people recommend for big overgrown lilacs is to prune out 1/3 of the trunks each year for three years, cutting them down to the ground. I think a similar strategy might work here. If it's a failure after the first year, the others will fill in and have better air circulation.

I have pruned my privets down from 9 feet, but i only cut them to about 3 feet. I am regretting that, and will try what i just suggested this fall.

There are several different kinds of privat but you should be able to cut them down down to nubs and they will come back. It will look awful for awhile but will then leaf out. I live in zone five and we trim to ground in early summer to give it time to start to grow before frost. Keeping privats at a certain height is high maintenance. I've trimmed mine 4 times already this year.

A neighbour had a 7' high vase shaped privet hedge for years. Last spring she cut it down totally leaving only 3 inch stumps. As of this fall it has grown to about two feet and is very bushy.
Tyler.

Yup. Saw it right down and start pruning it right.