I guess my concern is what that white noise is doing to the scilia in your ear. If it is strong enough to cancel say 50db, what is it doing to your ears?
Generally speaking, ANR won't work for gunshots. The noise cancelling ability does not respond fast enough to the shot to produce the "anti-noise" to compensate for it. That is why they are advertised for things that involve continuous, low frequency, droning sound such as the sound from engines, rushing air, etc.
If ANR was effective for gunshots, all the hearing protection companies would be offering them to shooters as this form of hearing protection would be superior to other hearing protection currently available.
I use the Peltor Tac 6-5 but not without foam plugs inside them. I got two sets at the BassPro outlet because I am sure someone returned them for "not working".
Great for skeet shooting in the winter. Keeps your ears warm as well.