No, you do not understand correctly.
Cruise altitude is limited by aircraft performance. The "optimal" cruise altitude (lowest fuel burn) is usually the highest possible.
Cruise altitude is also restricted by air traffic control. Today the airspace is separated into levels of 2000ft (in one direction). So an aircraft can climb from 31000ft to 33000ft as soon as it has
> the ability (lost some weight)
> the permission (by ATC)
The initial altitude depends on many factors (weight, number of engines, weather) and usually between 29k (B747-400 at max weight) and 37k (B737-700 on a short flight).
As people explained, there may be circumstances where you refuse a higher (= better) altitude. Weather may be one, as the turbulence margin shrinks with altitude.