I have a 97 840 and have been thinking of lowering the gear ratio... anyone have any information, gear recommendations? What model/year would be good for a straight swap?

3.64 or 3.91 are the two best choices.

If you can live without Limited Slip there are early 850 takeoffs in quite a few owners garages. Most of them switched to 3.91 LS from the stock 3.64 open differential original equipment on 850 automatics.

The 3.91 LS came only on the E34 M5 and are getting rather hard to find and very $$$$

There are some E32 750 3.64 LS units large case units available too.

I have 3.64 open in my 840 and am convinced that it was the right choice for me.

Can anyone tell me specifically where I can find a 3.91 or 3.64 bolt on application for 2 97 840's? I have access to a junk yard with hundred's of BMW's but you can't see the gear ratio unless it is removed from the car as the tag is on the top. So, I would need to know which car to look for or a company that would build me one with Limited Slip for less than $2000, which is the price I found so far.

If I remember right:
'91 and later E32 750 were 3.64 LS with the large case-Early is a smaller case that will not fit.

'91 E34 M5 was 3.91 LS was the only E34 large case.

There is a tag where the passenger side bearing retainer bolts on that gives the ratio. If this tag has an S on it it is Limited slip.

A large S printed on the case also indicated LS.

If the back cover is off then a LS has a silver assembly plainly visible across the center. The Open just has gears visible.

If you need to compare differentials out of the car-you are looking for a case that matches the E32 740 in size. The rear cover will be different between an 8 series and the 740 but the case is identical. E38s are different.

You can also research here http://bimmer.roadfly.com/bmw/forums/e31/search.php
This has been a hot topic on numerous occasions. Unfortunately the web site with the best info has gone missing.

You can also go 3.15 if you do not want too much.

I have my stock diff available if you want. I switched from my 3.64 to 3.91. e-mail me.

i have a 3.64 LSD for 250 shipped in 48 states