This is not really a Down Under query, but you're such a informed group...

On 737's, what control does the cockpit have over cabin pressurization?

I know on some more-engined aircraft, the PIC can run one or more ECU
units, with the result being more fresh air in/more frequent changes/hour
of the air.

But do they have pressure regulation control beyond On/Off? I thought
that differential pressure was regulated by the relief valve[s] at the
rear of the aircraft, and fixed.

I see a photo at <http://upload.wikimedia.org/wikipedia/commons/5/5e/Pxctl.jpg>
but...

I'm not taking on the Urban Legend about the [US-style] football player
charter where they were so drunk & roudy, the crew raised the cabin altitude
until they fell asleep; but rather an issue over can an airline skimp on
bleed air by the same approach. I don't think it's possible, but welcome
hard data.

Further, what altitide do the masks trip open?