What can be done to do away with bad breath besides good oral hygiene and perfect health otherwise?

The link below is to a good article '5 Tips to Combat Bad Breath':
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scrub your tongue, avoid mints and the like as they just produce more odor causing bacteria....use listerine and visit your dentist every 6 months.
Chew gum.
The problem might not be in the mouth. It could be in the stomach. Some food produce more gas than others.
if you have good oral hygiene and your breath is still bad...the smell is originating from bacteria in your stomach...your intestines should contain 3-5 pounds of friendly bacteria, but most people who have used antibiotics or eat a lot of sugar get an overgrowth of unfriendly bacteria whose byproducts create gases that lead to bad breath. try taking probiotics, flora, or friendly bacteria (all are the same thing...just different names)...any health food store can help you out.
Perhaps try taking some acidopholus capsules/Yakuit as these can be good for your digestive tract, helping to prevent your stomach from creating bad bacteria, through introducing good bacteria.

Also, anything that causes 'bad bacteria' will eventually cause bad breath! (eg. excessive sugar, cheese - yeast, other yeast products in excess like bread and bakery items) You don't eat a lot of pies, pastries and doughnuts do you?!
Chew fresh parsley on occasion