Why are many jet aircraft designed to cruise around FL350-370? If the flight distance permits, the B737-800 will cruise at FL350, the A320 a little bit higher... 


Flying at FL370. Photo: Live from the Flight Deck by GolfCharlie232 (reframed)

Elements such as time to reach cruise altitude, engine and airframe efficiency at this altitude, and acceptable cabin pressure surely influence the choice, but:


What are exactly the important criteria used, and the compromises made by engineers?
Would engineers choose other altitudes if the technology or any other current limits could be improved?
In a word, the tropopause.

Gas turbine engine efficiency improves with colder &amp; denser air. As an airplane climbs through the troposphere, the density &amp; temperature both drop, and the loss of density is more than offset by the lower temperature. Above the tropopause, however, the density continues to drop while the temperature holds (approximately) constant.

In the U.S. Standard Atmosphere model, this occurs at 36,089 feet. This represents a local (possibly global) optimum altitude for efficiency (and if there is a better optimum at a higher altitude, it's inaccessible for other reasons).