I'm reluctant to reply, lest we derail this thread. But from an A&I perspective, gas management for a dive to possibly 150' is an appropriate topic. Therefore breathing technique as it relates to gas management is also relevant.
A few terms have been put together that don't quite go together, physiologically.
We've got slow, shallow, deep, overbreathing, calm, narcosis, CO2 retention, airways and oxygen transfer, all in three sentences. Let's sort this out, with all due respect to the cumulative experience of the divers above.
Slow is good, up to (and maybe even including) the point of skip breathing. Without rehashing that argument, a slow rate with a hint of a pause at end-inhalation maximizes the time that oxygen is extracted from the alveoli and CO2 is discharged into them.
Calm is good, but shallow is bad. Period. If shallow makes you feel calm then there's a tradeoff happening.
Why is shallow bad? Dead space. You have pulmonary and equipment passages that are used but do not contribute to oxygen/CO2 exchange. The higher the percentage of your breath that you waste on dead space exchange, the more gas from your tank you are going to use. Why? Because to avoid hypoxia and CO2 retention, you must breathe some minimum amount. Any dead space ventilation is on top of that, but still pulls from your tank. From a dead space exhange standpoint, the most efficient technique might be one large breath per minute, large enough to dump all your CO2 and inhale all your next minute's oxygen at once, with long pauses at end-inhalation to allow the transfer to take place. But this is not physically possible. So we need a compromise.
Deep is good, overbreathing is bad. Slow breaths minimize the turbulent flow which is problematic at high gas density. Deep breaths minimize dead space exchange. Overbreathing (specifically, rapid exhalation) can contribute to airway collapse, which, while it doesn't affect oxygen transfer per se, does affect gas transfer, and therefore CO2 retention (and possibly hypoxemia) especially at depth (high gas density).
What are we left with?
A need to minimize dead space ventilation (bigger breath).
A need to minimize wasted ventilation (calm, Zen breathing).
A need to minimize turbulence at high gas density (slow breathing).
A need to maximize gas exchange (some sort of "pause" at end inspiration which won't screw up your buoyancy, but adds time for gas exchange at the alveolar/capillary interface), but which doesn't become skip breathing to the extent that your CO2 climbs from breath to breath.
Relatively Slow, Calm, Relatively Deep, and only what you need. That's how you minimize RMV.
