I don't have a Dremel Stylus, but I've been messing around with Dremel tools pretty regularly for more than 35 years. I just took a look at the instruction manual for the Stylus (Dremel kindly makes it available on the company website.) It's pretty clear that it uses the same collets that virtually all other Dremel Moto-Tools made in the past 40 or 50 years use. (They've apparently been changed a little bit - the sizes are now identified by rings around the shanks - but I'm pretty sure they're interchangeable.) Four different ones are available; they're designated 1/8", 3/32", 1/16", and 1/32". Those are the maximum sizes the collets will hold. The 1/32" one clamps down to zero. I've used drill bits down to #80 in Dremel 1/32" collets hundreds of times. (Caveat: I have a vague recollection of having bought, many years ago, a 1/32" collet that was defective, and wouldn't clamp all the way down. I took it back to the hobby shop. Another caveat: I've had my current set of collets for quite a few years; I suppose it's conceivable that the company has changed the way they're made since then. But I'm pretty sure that if your collet won't hang onto a #80 bit, either you've got the wrong collet or it's defective.) If you need a new collet and don't have a hobby shop within driving distance, try Lowe's, Home Depot, or even K-Mart. They often have Dremel displays, with racks of accessories including collets.
Machinists claim that collets are, by definition, more precise than adjustable chucks. I imagine those people are right, but I've also never had any particular trouble using small bits in a Dremel adjustable chuck. (Again - that comment is based on experience with quite a few older models, but not with the new Stylus.)
I hope I may be forgiven here for climbing up on one of my soapboxes and repeating a plaintive cry I've uttered quite a few times in this forum. Dremel tools are great, but for modeling purposes the blamed things turn too fast. Every time Dremel comes out with a new design, the literature hypes the speed and power of it. For modeling purposes - especially for those working in wood and styrene - every Moto-Tool is far more powerful than necessary. And the slowest speed on any adjustable-speed one is plenty fast enough - and the fastest speed is almost useless except in hard metals. (OK, at the slowest speed you can drill styrene and wood acceptably IF your bit is brand new and sharp. But if it's even slightly dull it will melt the plastic and burn the wood.)
I won my first Dremel tool in a model contest (the things were too expensive for an undergraduate student in those days) in, if I remember right, 1972 or 1973. It was a basic, single-speed model with a sleeve bearing, and when I fondled it in the box I thought I'd attained Nirvanah. Then I tried it out on the ship model I was working on, and discovered that the tool was almost useless - and, in fact, downright dangerous. So I scraped up the money to go down to the hobby shop and buy a "Tabletop Speed Controller." What a difference! This thing consisted of a little metal box with an electrical outlet on one side and a knob on the front. Plug the Moto-Tool into the outlet, plug the outlet into the wall, and adjust the speed with the knob. When the knob was turned all the way to the left, the tool stopped. I could turn the tool on, put the tip of the bit exactly where I wanted it with the bit sitting still, then gradually ramp up the speed until the motor was running exactly as fast as I wanted. Great. I eventually bought two of those "Tabletop Speed Controllers" - one for the Moto-Tool and one for my old Unimat lathe/drill press. They also worked for various other jobs in the shop: controlling the heat of a soldering iron, for instance, or even varying the size of the picture on a small black-and-white TV set. (Don't ask how I found that out.) I still have both of them; they still work perfectly. (The original, 1973 Moto-Tool worked fine - with one brush replacement - for at least twenty years, until the shaft-lock mechanism wore out. I suspect the slow speeds at which I ran it contributed to its longevity.)
Unfortunately Dremel discontinued the "Tabletop Speed Controller" quite a few years ago. (The company also used to make a foot-operated version, but it seems to be gone now too.) Other companies do, however, make speed controls that I suspect would work (though I haven't tried any of them). Example: http://www.woodcraft.com/Product/2003957/9183/Router-Speed-Control.aspx . The price is hefty, but in my opinion it would be worth it (assuming it works).
But Moto-Tools with built-in speed controls don't seem to get along well with accessory speed controls. Plug a modern, variable-speed Dremel into a speed controller and turn the speed controller's knob down to zero; the motor will stop all right, but as you turn the knob to the right, the motor will start jerking and sputtering, rather than smoothly ramping up to the speed you want.
A few years ago I found, at Woodcraft woodworker's supply, a nifty little gadget, made by a company called We-Cheer, called a "Micro Motor Detail Carver": http://www.woodcraft.com/Product/2003736/330/Micro-Motor-Detail-Carver.aspx . For model building purposes (styrene, wood, and soft metals, like brass and copper) this is quite simply the nicest rotary tool I've ever encountered. It's quite small (not a lot bigger than a fat pencil. The electrical cord is relatively thin and flexible. The hand grip is right down near the tip, so you can use the tool almost like a pencil. The regular speed of the motor is too fast, but the tool works fine in my beloved old Dremel speed controller. And one of the We-Cheer tool's bigges virtues is one that neither the manufacturer nor Woodcraft points out: it fits Dremel collets. If I were offering advice to a modeler just getting into power tools, I think I'd recommend this little tool (and some sort of speed control for it) as a first acquisition.
The other night I happened to be in the tool department at the local K-Mart, which had a modest assortment of Dremel products on display. Among them was an old-fashioned single-speed Moto-Tool. A sample was out where I could handle it; I was happy to note that the shaft bearing, though probably of the sleeve rather than ball type, seemed to be nice and tight. (On my first, single-speed model from 1973 the shaft slid back and forth at least 1/32". I don't think Dremel makes a single-speed model with ball bearings, but the sleeve-bearing version I examined the other night seemed to have virtually no play in it.) [Later edit: I checked the Dremel website. Apparently the single-speed model I was looking at does have ball bearings. Bravo Dremel!] I wouldn't trade my little We-Cheer "carver" for any Dremel Moto-Tool currently on the market (though I have a big, variable-speed Dremel for heavy-duty jobs - like grinding and routing), but my second choice probably would be that single-speed Dremel - with an accessory speed control of some sort.
Dremel has a nice website, with a users' forum. Some months back I used that to post my usual observation: the ideal Moto-Tool for the modeler would (1) be as small as possible, (2) have a speed range of zero (and I do mean zero) to 5,000 rpm, (3) be powered by a lightweight, long-lasting battery, and (4) cost less than $50.00. I never got a response from Dremel, and no other customers commented on my post. So I guess I'm in the minority. But I continue to think that any modeler who tries out my little "power carver" with its slow-speed capability won't want to go back to an elephantine Moto-Tool. Every Dremel product I've ever bought has been a high-quality piece of merchandise, but I continue to contend that the company just hasn't figured out - or isn't trying to cater to - the needs of the model builder.