Pulmonary breathing in top level athletes may be an important limiting factor of performance. 

Hemoglobin’s saturation percentage (Sa02) under rest conditions is close to 97-98%: this means that almost the totality of Hb molecules is carrying oxygen. 
SaO2 is easily measurable with skin oxymetry in the ear lobe, with the help of a little portable instrument. 

During high intensity efforts (at anaerobic threshold or above), hemoglobin’s saturation decreases to values comprised between 85% and 92%. 
This is particularly evident in well trained athletes, and it may be due to reduced times of alveolar gas exchange because of bloodstream’s high speed proper of athletes with big circulatory flow. 

At altitudes, the decrease in SaO2 is evident even in rest conditions, because of reduced atmospheric pressure that limits the oxygen diffusion from inhaled air to red blood cells passing by pulmonary circulation; it is not rare to reach values around 70% under effort in Hb saturation at an altitude of 2000m. 

It is believed that a reduction in SaO2 below 92-93% is sufficient to determine a significant decrease in VO2max: for every 1% decrease in SaO2 corresponds a reduction of 1% in VO2max, therefore of performance. (J.Appl.Physiol. 66:2491-2495,1989). 

SaO2 reduction under effort in some athletes is more pronounced than in others, with remarkable differences between individuals. 
I could personally check an SaO2 value of 79% in a strong professional cyclist performing a very high intensity effort at sea level (at the end of an uphill timetrial of approximately 17 minutes). 
Lance Armstrong never got below 92% in similar efforts, while at 2000m of altitude the same kind of high effort determined an SaO2 = 84%. At the end of a 2-week altitude training camp, Lance was able to bring this value up to 88%. 

Many studies demonstrated that pulmonary gas exchanges can limit performance for top level athletes: breathing a 26% oxygen enriched air mix (the air we breath has 21% of oxygen), the SaO2 did not get below 95% and the VO2max was 5% higher than basic values. 

It is likely to increase gas pressure in lungs’ alveoli with proper respiratory techniques, so to favor the passage of O2 from inhaled air to Hb molecules. 
Or maybe simply with an adequate hyperventilation under effort: it seems that many elite athletes do not hyperventilate enough when involved with high intensity effort. (Med.Sci.Sports Exerc. 32:926-932, 2000). 

This hypothesis is supported by the evaluation in such subjects of increased partial arterial pressure of CO2 (PACO2 above 35mmHg) accompanied by a reduction in alveolar pressure of O2 (PAO2 below 110mmHg). (J.Physiol.Lond 355:161-175, 1984).