In this photo it is rather easy to see that the bottom chamber of my bellows has approximately twice the volume as the top chamber.  This is contrary to the description in many books, but is more efficient of your "bellows pumping effort." This is not an original idea, I found this bit of information in an old book whose title I do not recall and must agree with the long ago author that this is the most efficient configuration.

     Equally sized top and bottom chambers will work you to death with no real benefit in air flow or control.  If it requires one full stroke to fill the top chamber, before it can begin shunting air to the fire, then you had better pump fast!  You need to refill the bottom chamber then fill the top chamber and do it before the top chamber is empty. Anything less and you will get a choppy air flow.  With the bottom chamber twice the size of the top, with one easy stroke, you fill the top chamber AND push air out to the fire.  Then you have the entire time it takes for the top chamber to empty into the fire to refill the bottom chamber.  It works.  I added one more flap valve to the bottom chamber than the top to ensure it fills fast.  A quick stroke and I am pumping a lot of air into the fire. 

One last caveat.  I found that if I extended the lever to give me a distinct mechanical advantage, it required a counter weight be place in the bottom chamber.  Otherwise the bellows will remain closed under the weight of the lever, alone. You may, on occasion, want to place a weight on the top chamber in order to speed the air delivery.  It will all depend on what you are trying to heat and how fast you wish to heat it.