By itself, not much. One thing you will want to keep in mind is you can't just slap on smaller SC pulleys (smaller size = higher blower rpm = higher boost) and expect more power. You need other supporting mods done in order to run smaller size pulleys.
On a bone stock 3800 Series II SC engine with stock exhaust, induction, and stock tuning, I wouldn't recommend anything smaller than a 3.5" pulley.
On the same engine but with free-er flowing exhaust and induction, you can get away with running a 3.4 pulley. However, I wouldn't run anything smaller than a 3.4 pulley on one of these engines without other mods being done. The type and amount of mods you have done will ultimately determine what size pulley you can run. But you need to keep in mind the faster you spin these blowers, the less effecient they become. (outlet temps go up as boost/SC speed increases). The end result of running too small of a pulley for the application can be detonation occurring which can lead to engine failure.
Personally, I would recommend doing the following mods in order...
1) Install larger exhaust system (also eliminate the bottlenecks that are present in the stock system)
2) Port the exhaust manifolds (front cast manifold needs the most attention) or install headers
3) Install 3.5" or larger cold air induction; eliminate sharp bends in the induction system if possible and use a K&N filter
4) Get the blower housing's outlet CNC ported and have an adapter made so you can run a larger throttle body like the 96-99 N* unit. Check out
www.tripleedgeperformance.com for very inexpensive SC housing porting and TB adapter services.
I would do all of the above before even touching the engine itself. If you were only going to do all of the above, I would say you could run as small as a 3.3" pulley with PCM tuning. Porting of the SC outlet lowers the SC discharge temps, reducing KR (knock retard, detonation). Running a larger throttle body (TB) will allow the blower to move more air without having to work as hard (boost can go up in some cases, so consideration in pulley size must be made here as well).
If you do all of this I would then look at doing other mods. Mods like higher-ratio roller rocker arms can increase valve lift and duration at 0.050" lift with little work but you need to watch your ratios. There are several rocker ratios available and I wouldn't recommend running anything more than 1.8 on stock low mileage springs. If your engine has high mileage, I would upgrade the springs anyway. There are some aftermarket cams out there that will work with the stock springs, but most will not; and of course, replacing the cam is a much bigger job than just replacing rocker arms. If you decide to upgrade your valve springs you need to watch the spring rates. Higher rates will put greater stress on the lifters, camshaft, and timing chain components; thus reducing their life expectancy and durability. So you will want to keep that in mind as well.
Of course one of my favorite mods would be pulling the heads off and porting them; however this is one of the most expensive mods to have done if you can't do it yourself. The bonus here is, if you know what you are doing when head porting, you can increase engine power without sacrificing drivability. If you haven't had any training on head porting or don't have much experience, this job is best left to the professionals. It is very easy to make a set of heads flow WORSE if you remove too much material or remove material from the wrong places in the ports.
These examples are just a few of the things you can do to increase the power output of a 3800 SC engine. As with any engine, you need to find the right balance of parts so everything works together. The size of the SC pulley is no exception. Therefore you really can't say how much more power a particular size of SC pulley is going to gain you. It depends on many other factors.
The above is based on my recommendations. Other people might have different recommendations but what I have said above is what I have personally tried and found to work the best with the least amount of investment. Of course there is much more you can do to get more out of these engines, but this should give you a pretty good idea of what you are looking at.
-ryan
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power corrupts. absolute power corrupts absolutely. 
Custom Computer Tuning | Engine Conversions | Turbocharging | www.gmtuners.com[This message has been edited by Darth Fiero (edited 11-29-2006).]
