I don't know what it is like with the electric or gas smokers, but with the Weber... less smoke is sometimes more...
I use maybe 2 small fist sized chunks of wood (usually cherry or oak/fruit wood) for the entire process. Once the Weber is up and running stable, you really don't see any smoke coming out the top, just a thin, bluish vapour. You don't generally want to be adding smoke wood all the time as you can easily overpower some meats (especially fowl). This is "hot smoking" or BBQ'ing though.... 220-250F. Although I routinely do pork shoulder and ribs above this temperature with fantastic results.
Burt