Captain's notation concerning the Luchard being limited to a maximum of 2800 psi due to being a 3 stage pump reminded me how far the engineering of compressors has come since the 40's and 50's designs. With the right balance of factors such as piston sizes, appropriate interstage pressures and compression ratios, better cooling and the correct rpms for a given system, the max pressure limitations of 3 stage units are way up there now.
Since at least the 70's 4500 psi 3 stage units have been readily available to the breathing air industry (including diving use). That soon moved up to 5000, and for at least 10 or 15 years now Bauer has been producing a small 6000 psi 3 stage compressor by making just a few design changes to their 5 cfm "Capitano". I don't recall what changes may have been made in piston bore sizes, but they did slow the rpms down to the point it only produces about 2.5 cfm (by my actual flow meter readings on 4 or 5 different compressors)... never mind that they used a model designation of "H5" to make us believe it was a 5 cfm unit. A good number were sold to fire departments as such, and they are pretty inadequate in all but the smallest departments in small towns. I will say I have been pleasantly surprised at how cool these little beasts run at 6000 psi. Way cooler than their popular 4 stage 6000 psi unit running at 10 cfm (they call it 13). Five stage compressors have a big advantage in lower compression ratios and less heat. In the mid-70's we were using a 15 cfm 5 stage Joy at the dive shop and even after filling several tanks to 3000 you could hold your hand on the final stage head. It was not even slow turning, being direct driven at about 1700 rpm by 20 hp motor. It still works.
"I get plenty of excercise just pushing my luck!"