Graeme Obree, an Absolute Genius whom the UCI smothered and buried, describes and recommends in his book "The Obree Way" an interesting breathing technique developed by him over the years. 
Already in my article "Pulmonary Breathing" dated 09/06/2005, I emphasized how very often athletes, even top-level ones, do not breathe efficiently especially under intense effort (Med Sci Sports Exerc 2000, 32:926-932). 

Obree observes how often cyclists under effort instinctively tend to gasp and generally breathe in a not very efficient way, in particular by not emptying the lungs completely during exhalation. 
This means that residual air, low in O2 and rich CO2, mixes with fresh air rich in oxygen, consequently "impoverishing" alveolar pulmonary gas exchange. 

Graeme therefore describes his technique which includes three breath cycles to be repeated in succession: 

- start with a FULL EXHALATION to empty the lungs from residual air 
- proceed with a deep inspiration to "fill up with fresh air" 
- continue with the second respiratory cycle (exhale-inhale) which will have a depth half of the first 
- the third cycle will have a further lower depth 
- finally resume the sequence again with a full exhalation and deep inspiration. 

Obree recommends to focus particularly on the diaphragm, which must "pump up the lungs like a bellows", especially in the exhalation phase. 
He suggests to exhale with your mouth and breathe in with your nose and mouth together. 
He further points out that this breathing technique should be trained for at least a month, so that it becomes automatic, and states that if properly applied it is able to improve the aerobic performance by 3-8 %. 

A recent article (Exp Physiol 2012; 97:311-318) reports that the cost of breathing for top-level athletes can be up to 15-16% of VO2max, when engaged in an intense effort. 
This explains, at least in part, the suggestion of Obree to limit oneself to a forced exhalation-inhalation every three breathing cycles, in order to reduce the energy cost of breathing. 
The same article emphasizes the importance of respiratory muscle fatigue, which is the cause of a vasoconstrictor reflex on the muscles of the lower limbs (see also J Physiol 2000, 529:493-504), effectively restricting the flow of blood and thus oxygen. 
This observation draws attention to the opportunity of training the respiratory muscles, but this deserves another article.