Specific heats at high pressure

I just got the book "Mechanics and Thermodynamics of Propulsion",
mostly on the recommendations found in the sci.space.tech archives. I
turned to Appendix 2 to find tables with specific heat vs temp for the
various gases that you find in a rocket engine (O2, CO2, CH4, H2, H2O,
that sort of thing). Hooray!

Imagine my disappointment when I noticed that the tables were
specifically for gases at low pressure -- 1 atm. That pressure
doesn't come up very often in simulations of rocket engines and
hypervelocity guns.

I've looked on the web, but have not found a reference for specific
heats of these gases at high pressures. I'm mostly interested in the
100 - 1000 atm range.

Am I just being stupid or unread? Is there some bog-standard
adjustment that I'm supposed to make to these specific heats to
account for pressure? Or did some guy in 1886 prove that specific
heats are completely independent of pressure?