Going by the pictures, and the info you've provided, my SWAG is that you may have a No. 40 New Model pocket rifle with a cut back barrel. 

Also appears that the rear dovetail sight, which should have been a tangent style, was swapped out with a Stevens #106 leaf rear, or a Lyman #6 rear that is missing the "bar" leaf. 

I'm leaning toward the Lyman #6 with the missing leaf, as the single leaf appears to be slightly offset forward of the pivot screws, though my photogrammetry skills may be a bit out of alignment today. 

And this SWAG is worth exactly what you paid for it.   

Keep the pictures coming. Definately interested. I have a similar gun that I am currently working on. I think mine was also shortened to 8" as I recall. John Taylor currently has it making a new extractor. I had him reline mine and recomend him highly if you choose to reline it. Stocks are hard to find but are out there. I bought the stock for mine on GB because the price was right and ended up buying the gun it came off from the same guy and ended up bringing it back to a shooter. These are neat period pieces and fun to shoot. I have a really nice one in .32 Rimfire. Ammo cost is a problem with the .32 but fortunately I bought some Navy Arms ammo back when it was available.
Keep us posted and have fun with it.

Slumlord, there's a  Pocket Rifle in 32 in my neck of the woods about 95% condition with the stock and a velvet lined custom case--asking price is @ $1100.00--but was a little steep for my gun budget right now (bought a few too many High Std. pistols recently--one of my other weaknesses)  and, like you, I like to shoot my guns and didn't want to get in to having to source 32 ammo or converting it to 22.
Come to think of it, I know of 2 Favorites in 32 as well at KTP in Me., maybe someday someone will make another batch of the stuff for guys like us that like to shoot them.

PS--have John check the firing pin bushing too.  Took it out for the first time tonight and the "lip" on the bottom front was broken off--that forms the slot the screw goes through to keep the bushing from just coming out--yet it had functioned OK for about 150 rounds so far.
It was too small to silver solder back on, so I just built up some phosphor bronze / silver alloy solder and filed it back to shape--so far, so good!

Work in progress--here's some more pics;
I have the barrel stripped and polished, and playing with the sights;
First, the pics actually make the parts show up a little worse than they look in real life--some of what appear to be pits and file scratches remaining is really just dust and fingerprints--I was in a rush to do the pictures.  Notes are;
Barrel was polished starting with 220 sand paper, then 400, 600, 1500 wet or dry paper, then Simichrome polish on a rag, by hand.  I use my favorite tool--a piece of paint stirrer stick with the paper wrapped around it to help apply more pressure more evenly.  I seems in one place already filed through the nickel long ago, that if I polish it well enough the polished steel blends right in with the old nickel.  Of course at some point I may well send it out to be re-plated anyway.
Barrel--waiting for some Brownell's Oxypho to come in, so hopefully by next Wed. or so the barrel will be blued.  I trued the muzzle with a file (it was 1/16" off with file marks under the patina from an old cut back job) and I crowned it with a round head screw in a drill using Napa water based valve grinding compound, then polished with 400 grit wet or dry wrapped around a sharpened pencil.
Sights--front sight is an unknown 3/8" dovetail metal sight I had in kicking around that looked to be a good height--used a file to trim it down to the 5/16" dovetail on this gun.  Sight is not final fitted yet--any misaligned grooves you see will be taken care of before final polish, blue and fitment are done. I will round the corners to blend with the barrel.
Rear sight;  The original rear sight leaf was loose and floppy and screws were stuck.  I heated the sight gently with a torch three times a day for 3 days and then soaked it in a mix of 1/3 Liquid Wrench and 2/3 Kroil after each time, then let soak for 2 more days--the screws came right out.  I may go to Marbles adjustable sight as a shooter for better sight picture. Pics to follow in the next post

Steve,
Nice pistol and nice clean-up without being over agressive. Did you notice any lateral loosness of the barrel at the pivot point? Question based on experience with a similar type that was difficult to keep tight with use.
Chuck

Shooting single shot pistols.  Right handed shooters. Place the pistol across the left forearm grab the your shirt push forward with the left arm and pull back with the right.  You will have a very solid off hand position.

Det

Steve,
Thanks, says something about the quality of the Stevens. The one I was messing with was similar but not Stevens.
Chuck