There has been some recent discussion ( again...) on this subject at the c.net forum ("Teaching and learning")

http://www.concertina.net/forums/index.php?showtopic=10421

A few comments:

jggunn said(#1):" There appears to be some distinct differences of opinion about this matter. Some advanced tutors and players suggest that using the bellows to articulate a note is close to a sin and can be not only detected by the trained ear but is technically incorrect".

RE:A misunderstanding? or somewhat peculiar "advanced tutors"...!? All since "advanced" tuition for squeezebox playing was initiated the terms ( or similar) "finger articulation" and "bellows articulation" have been described and established as basically different but equally important and 'correct' methods for starting and ending a note. Bellows articulation particularly important for the most sophisticated and sensible expression since by finger articulation one can only start or stop the sound, hardly form it at all !

Alan Day said(#3):"He ( = Goran/myself)) recommends this style of bellows action as he states that it gives more control of the bellows particularly when playing an English or Duet for quick movement of the bellows in and out".

RE: Some modifications:By the term "bellowsing" I have meant ALL activities and variants using the bellows - what most tutors call "management of the bellows" (which I think is an awkward expression).
"Bellowsing" fits "fingering","holding","supporting",carrying" and so on and was once choosen because of opposition against my first suggested term "bellowing" - meant having funny associations

The "style" Alan refers to is the particular method "bellowsing" by "fanning" the bellows by keeping one part of the bellows closed and possibly facilitating the process by using a "cross-the-bellows-strap" like I have demonstrated.

Jim Lucas said:(#7):"But I personally find that it doesn't give me more control. Instead, I find it limiting, particularly in terms of dynamic "punch", which I can do with much greater strength using a straight in-or-out motion than the rotational motion of fanning".

RE:A comment from someone who has not investigated the matter thoroughly - neither in theory, nor in practise!

Theory: Everyone with elementary knowledge in mechanics is familiar with the importance of stability. Recall Archimedes from your school books! Fanning the bellows increases the stability and consequently the control.This has impact both on controlling the pumping and controlling the fingering since the connection between the player and the instrument benefits from the method.

Practise: It is very easy to find out but one has to overcome old habits and be openminded and criticial when trying out any 'new' way of doing what has been habituated otherwise for a long time!The easiest way to understand the significant advantage by "fanning" is using a "cross-the-bellows-strap".
One detail has to be kept in mind: The maximal volume capacity of the bellows of course is restricted by fanning and when this musically IS important as when playing polyphonic legato hymns or similar things depending on the model of instrument one may have to use "straight" bellowsing.
The improved control by fanning however mostly compensates generously for the restricted volume and the greater general efficiency means that it mostly is superior to straight bellowsing.
As m3838 said (#17) pointed out there are important anatomical advantages as well but the significance thereof depends on the occasional stature and posture of the player.
Goran