BMW X3 - Smoke Sometimes from the Tail Pipe

"White smoke from the tailpipe is almost always a sign that you're burning coolant, usually via a failing/failed head gasket. Check your coolant level to see if it's decreasing. If this behavior has only recently started, it might take a bit of time before you get the 'mayonnaise-like' residue on the oil filler cap, or the coolant level drops enough to reach the point where the engine begins to overheat.If it is the head gasket failing, I probably wouldn't let it go for long. If the coolant (which is at least 50% water) is mixing with the oil, that's probably not keeping your engine well-lubricated, it's certainly not doing your catalytic converter any favors, and you're just inviting any number of other problems (engine overheating, hydrolock, etc.)..."

"CVV failure also produces white smoke, and the key factor is if it's only on start up and if it's not losing coolant, we could rule out head gasket."

http://www.bimmerfest.com/forums/showthread.php?t=578689

http://www.bmwbuddy.com/z/part/11617533400-bmw-crankcase-vent-valve-pressure-regulating-valve

It may look like smoke, but actually is steam , which is normal in cold morning. Steam is a also a product of combustion beside CO2.

Improve its diet - a cup of coffee and a cigarette do not make a good breakfast.

Oil running down the valves can also cause the condition observed. Oil return holes in the head that are restricted will allow oil to surround the valves, making the situation worse.

Try to determine if the smoke is steam from combustion, from coolant, or worse. A clean white rag across the tail pipe may help to decide the contents. If it is coolant, it will show up as coolant levels drop. If it is oil smoke, the engine oil level will drop, and the stains on the white rag will be oily. If it is just condensation from combustion, it will be worse on cold mornings, and lighter, or nonexistent on warm mornings. What is the air temperature when the smoke is at its worst?

C'mon guys, the OP said "smoke", SE added that it was white. Nobody asked how many miles/km were on the engine, whether there was recent engine work, where it's located, what the weather is, how long the smoke lasts, etc.

While I agree with most of the guesses above there's also the possibility of normal catalytic converter warmup that releases steam that does condense into a cloud on cool mornings, or the possibility of worn or leaky valve stem guides, or missing/improperly fitting stem seals/wipers.

Where I'm located a tailpipe dripping water and/or spouting a white cloud simply means that the engine was was just started, is operating open-loop, and has not reached operating temperature.

OP, do you have more details to help us out?

If it's a puff when you first start it up and it is an automatic transmission, it might have a thingy called a 'vacuum operated modulator valve' which has a rubber diaphragm in it that might have a split in it allowing a few drops of transmission fluid to be sucked into the intake via the vacuum hose.

I'm a Chevy/vintage British guy so I've never owned any Beemeers so I'm just guessing.

The smoke would be blue.

I had a 1988 Chevy pickup that did this.

I replaced the valve seals and the problem went away.

I had a Dodge van that did that. I replaced the van and the problem went away.