An altitude compensating nozzle is a class of
rocket engine
A rocket engine is a reaction engine, producing thrust in accordance with Newton's third law by ejecting reaction mass rearward, usually a high-speed Jet (fluid), jet of high-temperature gas produced by the combustion of rocket propellants stor ...
nozzles that are designed to operate efficiently across a wide range of altitudes.
Conventional designs

The basic concept of any engine bell is to efficiently direct the flow of exhaust gases from the rocket engine into one direction. The exhaust, a high-temperature mix of gases, has an effectively random momentum distribution, and if it is allowed to escape in that form, only a small part of the flow will be moving in the correct direction to contribute to forward thrust.
An engine bell works by confining the sideways flow of the gases, creating a local area of increased pressure with a region of lower pressure "below it". This causes the gases to preferentially flow in the direction of decreasing pressure. By careful design the engine bell grows wider so that the pressure decreases in such a way that by the time the exhaust flow has reached the exit of the bell, it is traveling almost completely rearward, maximizing thrust.
The problem with the conventional approach is that the outside air pressure also contributes to confining the flow of the exhaust gases. At any given altitude, which is to say, at any given ambient air pressure, the bell can be designed to be nearly "perfect," but that same bell will not be perfect at other pressures, or altitudes. Thus, as a rocket climbs through the atmosphere its efficiency, and thus thrust, changes fairly dramatically, often as much as 30%.
Altitude-compensating nozzles
Altitude compensating nozzles address this loss of efficiency by changing the shape or volume of the rocket nozzle as the rocket climbs through the atmosphere. There are a wide variety of designs that achieve this goal, with the aerospike being perhaps the most studied among them.
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Aerospike engine
The aerospike engine is a type of rocket engine that maintains its aerodynamic efficiency across a wide range of altitudes. It belongs to the class of altitude compensating nozzle engines. Aerospike engines were proposed for many single-stage- ...
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Plug nozzle The plug nozzle is a type of nozzle which includes a centerbody or plug around which the working fluid flows. Plug nozzles have applications in aircraft, rockets, and numerous other fluid flow devices.
Hoses
Common garden hose trigger nozzles ...
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Expanding nozzle
The expanding nozzle is a type of rocket nozzle that, unlike traditional designs, maintains its efficiency at a wide range of altitudes. It is a member of the class of altitude compensating nozzles, a class that also includes the plug nozzle and a ...
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Single expansion ramp nozzle
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Stepped nozzle
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Expansion deflection nozzle
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Nozzle extension
Other methods for altitude compensation
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Multistage rocket
A multistage rocket or step rocket is a launch vehicle that uses two or more rocket ''stages'', each of which contains its own engines and propellant. A ''tandem'' or ''serial'' stage is mounted on top of another stage; a ''parallel'' stage is ...
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Tripropellant rocket
References
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Rocket propulsion
Nozzles