I could not achieve "zero" nitrates until I added a 6-7 inch deep sandbed. Bacteria will become established in the oxygen depleted area deep in the sand bed, if it is this deep. The bacteria will feed on the nitrates, converting them to Nitrogen gas, that bubbles out into the atmosphere. It will not harm you to breath it, as our air is already mostly Nitrogen.
A DSB is not necessary to achieve 0 nitrates. I have basically a bare bottom 40 breeder and have 0 nitrates. Could you give us more information on your set-up, so we can try to figure out the source.
Water changes definitely help to bring down nitrates.
What protein skimmer are you using? A good skimmer is one of the best ways to keep nitrates down. It doesn't remove nitrates but it will eliminate things before they get a chance to break down into nitrates.
The best IMHO way to reduce nitrates to unmeasureable levels is to increase the nitrate consumers. I recommend macro or other algaes for that. Plant life also consumes phosphates, filters out toxins like heavy metals, stabilizes operation, returns carbonates as it consumes nitrates, and consumes carbon dioxide and returns oxygen so that in a 24 hour period the tank becomes a net consumer of carbon dioxide and producer of oxygen.
it's a 40g tank with a visi jet ps100 protein skimmer 20lbs of live sand, and about 50lbs of live rock. it has a Foxface and a Volitan Lionfish in it. the tank is temporary only. I will be getting a 85g+ soon.