You just need more plants. A reef tank will try to correct itself by growing more plants, but they may not be plants you like to see or plants that overgrow your coral. I set up a 24 gallon nanocube for my grandmother about a year ago. It has acropora, montipora, zoanthids, pulsing xenia, mushroom polyps, stylo pistillta, star polyps, a percula clown, a pacific blue tang, a watchman goby, a purple firefish, an axelrod blenny, a blue damsel, a cucumber, several peppermint shrimp, a cleaner shrimp, a dozen blue reef hermits, an emerald crab, lettuce slugs (reproducing), a red linkia star, a globe urchin, brittle stars and comet stars (reproducing), as well as a host of amphipods, isopods, copepods, annelid worms, tube worms, limpets, flatworms and many other liverock hitchhikers. My grandmother likes to feed it heavily at least three times a day and the fish are growing quickly. The filteration is accomplished by the growing of many different plants and some bateria, but primarily by a bunch of caulerpa taxifolia. This plant is used because is looks good and grows quickly. Clever placement and periodic harvesting prevent it from overgrowing the coral. Zero water changes have been done. Lugol solution (iodine) is the only additive, although I imagine the hard corals would grow a lot faster if some calcium were added. If you don’t add the iodine for long enough the pulsing xenias stop pulsing.
So a heavily stocked small tank can work this way even for my grandma, who mostly doesn’t know what she is doing. You just need to set it up correctly in the first place. This is a matter of getting the right number of decomposers and eaters of each type of algae so that it is balanced. Some of it is art and experience, but some is just trail and error on each system. I like to balance things by moving snails from tank to tank as required until a new tank stabilizes. Populations of little things will find equilibrium for you usually in a couple weeks if you include some well established live rock at the beginning. Live rock you buy in the store, I find is usually mostly dead. If you move rock from another established reef tank you will get adult animals instead of just eggs. Also worms are very important. A strong population of bristle worms is healthy component of any reef tank; just try not to touch them. Typically any fish will keep them mostly in hiding during the day because they fear movement. That way they won’t be crawling through a plant you are trying to harvest.
The plants will take care of any nitrate problems within hours. Micro algae can scrub it down to a few parts per billion, much less parts per million. For larger systems I designed and built my own Algal Turf Scrubbers since I couldn’t buy them. Unfortunately they are not for sale anymore due to legal hang-ups on the patent.
Like waterkeeper says, many different techniques can be made to work. I would just add some more plants. What do you have now? What types of algae? Where does it grow? What is eating it?
