I guess I should probably add - the smaller the better. I'd really like to keep it under 7" long and 3/4" thick, so it fits in the case. LOL!
I'm going to have to do a lot of research after I get all of this feedback!
Shopping for MODs is big fun. This site has a whole lot of them listed.
Electronic Cigarette Mods | e-Cig Mod Reviews and Comparison
That 3/4" width constraint really narrows the playing field down alot. Most mods that take 10440 sized batteries will probably be small enough, but that size battery really doesn't hold much of a charge. It's barely a step up from the stock batteries. If you step up in size to a 14500 or a 16340 battery, those have pretty good capacity AND they have to ability to drive LR attys to their full potential, in particular the IMR chemistry batteries in that size. Get AW batteries, they're simply the best.
Fyi, battery designations indicate their dimensions, for example an 10440 is 10mm wide by 44mm long and the trailing zero indicates round.
I've got two 16340 MODs, the Chameleon (from IkenVape) and the Mini-VapeStack (from MadVapes). Both small simple fixed voltage single battery MODs. I like the Chameleon because of its small size, button placement, full set of 510/901/801 adapters, battery capacity and power. But even the width on the more slender Chameleon is right at your 3/4" constraint.
Some models with >10440 batteries that might be slim enough. These are all listed (with links) on the site linked.
* Chameleon - 16340 (right at your 3/4" constraint)
* Precious M - 14500 (pretty certain this is slimmer)
* Precise 16 - 16340 (pretty certain this is slimmer)
* Mako Midi - 14500 (not sure, but maybe a little wider)
* VYPR - 14500 (not sure, but i think slimmer)
Have fun shopping!
Also, if your not looking for increased power, but instead want to extend the experience of your stock 510 batts... definitely consider the eGo/Riva since those provide the same regulated voltage output as the stock 510 batts (around 3.1v), but will do so for longer.