Here is what I do and it has worked very well for me. I will take the wood that I need for the current smoke, cut up into splits about 3" diameter by 14-16 long. I will set these in a big metal tub and use my weed burner to char them fairly well, to the point where the surface starts to "crack".
Once they are charred, I use them for the smoke. This does a couple of things, it burns off any nasty stuff that may be on the wood, it helps to burn away some of the compounds that give you billowing white smoke, and it helps to dry the wood even further.
Personally, I think the closer the wood is to its prime for good combustion, the better, however, others have good results by just adding unburnt splits to their fire. This particular method, like I said, works for me and I no longer have the problem of white smoke when I add wood.
I will also keep a few pieces inside the firebox, away from the flames, next to the door on the firebox. The wood is heated up and close to the temp where combustion occurs. Being kept hot like that, when its time to add a piece or two, when I toss them on the fire, they ignite almost instantly. Other do the same thing with "UNBURNT" splits, by simply placing their wood on top of their firebox. The wood heats up, burns away some more moisture in the process, and when its time to add more wood to the fire, the time it takes for the wood to ignite is greatly reduced.
I had a pic of how I do mine but I cannot find it on here.
I look at it like this.
Say you have a pot of boiling water, 212 degrees, and next to it, you have a pot of cold water. If you add the cold water to the boiling water, it stops boiling and takes a while for the water to begin boiling again.
Now, if you have the same pot of boiling water, and add to it, water that is 200 degrees, (2 degrees below the boiling point) the amount of time it will take all the water to reach 212 degrees in order for it to boil is greatly reduced.
Just like the wood, the closer it is to the combustion temps, the sooner it lights, and the sooner it lights, the less the white smoke.