I'd like to kill the "they primarily only eat copepods" myth right there.
What is true for Mandarins is that they primarily feed on "live food". But their diet consists of much more than copepods, and includes other types of pods, small snails, worms and even fish eggs.
And this is factual information based on gut content analysis of wild specimens.
Now with that out of the way...
We move into territory based on my observations and personal experience.
Dragonets can actually quite "easily" be maintained in a 30 gallon tank, and even tanks as small as 10 gallons for individual specimens.
HOWEVER, the tank must be designed from the ground up to cater foremost to the Mandarin's dietary needs, and that actually means keeping a somewhat "dirtier" tank than normal, dominated by different kinds of macro algae and a fair amount of live rock.
You want high nutrient levels that will basically put the entire food chain in the tank into overdrive. This also pretty much means kissing anything but the hardiest of corals goodbye.
Extremely fine live sand in such a tank is also something that is essential in such a system IMO, as it creates a perfect medium for tiny invertebrates to live and reproduce in and an ideal hunting ground for dragonets, as they will actually flush sand and detritus through their gills, separating it from a tasty morsel which they "most likely" clamp in place with their pharyngeal jaws.
https://www.youtube.com/watch?v=1Ydk7avCyx4
Now I am also however a firm believer of "supplemental feeding" regardless of the tank size, as I believe it unethical to just simply let them fend for themselves and hope for the best.
And for ease of use I like using Frozen Lobster Eggs(though I hear you can't get them in North America, so something like Nutramar Ova is comparable)
Supplemental feeding accomplishes two goals I have.
1.) It helps offset any downturn in their success hunting for the day and ensures they get at least one or two solid meals that meets their nutritional needs every day.
2.) Any surplus food enters the food chain and directly feeds the living critters the mandarins feed on.
Now I'd also like to point out that proper husbandry and maintenance is key. Don't take "high nutrients" as an excuse to just let things lapse. Basically you want the system packed with macroalgae showing healthy growth, even a fair amount of microalgae is a good sign.
There should be just enough nutrients in the system to fuel explosive growth of the desired algae you cultivate, but no more. If you see nasties like Cyanobacteria and Hair algae show up then that means it's time to look over your maintenance routines.
Now I really hope I've managed to actually say something useful and cohesive here and that it does not all just come across as the ramblings of a mad-man. :spin2:
And here's also a little picture of my 29g Mandarin Tank and my original 10g Mandarin tank before the upgrade.
John, Alex raises some very good points, however, there are a few things to clarify:
Wild caught mandarin have been found to eat things like small snails, amphipods, copepods, small worms, however, this is done with a much larger system than a household reef tank. Within the home aquarium, creatures such as copepods and amphipods are much more common, but not small worms or small snails that are self sustaining for a mandarin.
Most mandarin fish currently in the trade are wild caught (the exception to this are the ORA captive bred ones, which are more difficult to find), which means they are used to live food. As I said before, they can be converted to frozen, but not all mandarin will willingly convert to frozen very quickly, mine took months before it did. There are those that have been lucky in getting a mandarin that'll start eating frozen or pellet right away, but, don't walk into owning one assuming it'll start eating frozen right away, make sure you have a backup plan for some form of constant live food. My mandarin will no longer eat copepods as it seems to prefer the live brine and frozen I feed it, but, don't assume it'll start eating it right away. Many people have had these fish die of starvation because they assumed this.
Also, for the substrate, very fine sand is not required, but, with not using fine sand, there is a slightly higher risk of the fish chocking. I currently have crushed coral substrate and that has worked just fine for generating pods and my mandarin sifting through it.
For copepod reproduction, as Alex stated, a high nutrient system is better, but, what he means by a high nutrient system is that there is always something for the copepods to eat (left over food, phytoplankton, or fish poop). These things will result in higher nitrate and phosphate levels as the phyto, food, and poop break down, and it's the nitrate and phosphate levels you will need to watch (it's the nitrate and phosphate that leads to the algae blooms and fish stress). Macroalgae will help with this because the macroalgae consumes the nitrate and phosphate to live. In addition the macroalgae serves to be a hiding place for amphipods and copepods to live and reproduce, however, there are many fish which will skim the surface of the macroalgae and take the pods off the surface, and there are some fish which will plunge head first into the macro to get to the pods. I've had quite a few fish which did this regularly. Also, the added nutrients will not make each copepod reproduce faster, what it does it prevent more of the babies from starving to death before they become adults and reproduce themselves.
Additionally, in regard to copepod reproduction, as said, there are two primary copepods a mandarin will go after, tisbe and tigriopus californicus (tigger pods). It takes approximately 8-12 days for a tisbe to go from newborn to reproduction age, and it takes tigger pods about 21 days to go from newborn to reproduction age. Now, knowing that a mandarin can go through thousands of pods a day, you will need a substantial number of pods to begin with so they can grow and reproduce faster than the mandarin can eat them.
As a long term goal, supplemental feeding is a very good idea, and when the mandarin converts to frozen, I've seen people have luck with gut loaded frozen brine, bloodworms (my mandarin won't touch this though), mysis shrimp, fish eggs and prawn eggs. Nutramar Ova (which is prawn eggs) had been an almost magical food for a lot of people because it seemed many fish were easier to convert to frozen using this, but, there is now a worldwide shortage of prawn eggs, and, because of this, Nutramar Ova is not currently available. If you're lucky, you may be able to get some form someone who has some in their freezer.
The key here is to make sure the mandarin always has food in it's stomach. What I have observed with my own mandarin is if I feed it to the point of it's stomach being engorged and it stops eating (basically it's full), about 2 hours later, it's ready to eat again.
All of this is making it seem more complicated than it really is, but, I want you to be successful, so the best thing I can do is give you as much information as I can to make sure you're prepared. I'd really like to see more people have success with these little fish in smaller tanks, but, no matter what system you have you have to deal with the reality of what the fish is, something that either needs to graze on food all day (on things such as copepods/amphipods) or will need to be fed until full a few times a day (for it being healthy and fat, I'd say feed it until it's full no less than 3 times a day, but the more the better).
Good luck.