Question: Why are rebreathers useful for such things as underwater photography and covert work?
About the article "Scuba diving", section "Rebreather".

Candidate passages:
Media Diving is a term used to describe divers engaged in underwater photography and underwater cinematography outside of normal recreational interests.
Media Diving is often carried out in support of television documentaries, such as the BBC series Planet Earth or Hollywood blockbusters, with feature films such as Titanic and The Perfect Storm featuring underwater photography or footage.
Media divers are normally highly trained camera operators who use diving as a method to reach their workplace, although some underwater photographers may start as recreational divers and move on to make a living from their hobby.
Equipment in this field is varied with scuba and surface supplied equipment used, depending on requirements, but rebreathers are often used for wildlife related work as they are normally quiet, release few or no bubbles and allow the diver a lengthy bottom time with a reduced risk of frightening off the subject at hand. 
Less common are closed circuit (CCR) and semi-closed (SCR) rebreathers, which unlike open-circuit sets that vent off all exhaled gases, process all or part of each exhaled breath for re-use by removing the carbon dioxide and replacing the oxygen used by the diver.
Rebreathers release little or no gas bubbles into the water, and use much less stored gas volume, for an equivalent depth and time because exhaled oxygen is recovered; this has advantages for research, military, photography, and other applications.
Rebreathers are more complex and more expensive than open-circuit scuba, and special training and correct maintenance are required for them to be safely used, due to the larger variety of potential failure modes.
In a closed-circuit rebreather the oxygen partial pressure in the rebreather is controlled, so it can be maintained at a safe continuous maximum, which reduces the inert gas (nitrogen and/or helium) partial pressure in the breathing loop.
Minimising the inert gas loading of the diver's tissues for a given dive profile reduces the decompression obligation.
This requires continuous monitoring of actual partial pressures with time and for maximum effectiveness requires real-time computer processing by the diver's decompression computer.
Decompression can be much reduced compared to fixed ratio gas mixes used in other scuba systems and, as a result, divers can stay down longer or require less time to decompress.
A semi-closed circuit rebreather injects a constant mass flow of a fixed breathing gas mixture into the breathing loop, or replaces a specific percentage of the respired volume, so the partial pressure of oxygen at any time during the dive depends on the diver's oxygen consumption and/or breathing rate.
Planning decompression requirements requires a more conservative approach for a SCR than for a CCR, but decompression computers with a real time oxygen partial pressure input can optimise decompression for these systems.
Because rebreathers produce very few bubbles, they do not disturb marine life or make a diver’s presence known at the surface; this is useful for underwater photography, and for covert work.
The closed-circuit type filters, supplements, and recirculates exhaled gas: see rebreather for more information.
It is used when a longer-duration supply of breathing gas is needed, such as in mine rescue and in long tunnels, and going through passages too narrow for a big open-circuit air cylinder.
Before open-circuit SCBA's were developed, most industrial breathing sets were rebreathers, such as the Siebe Gorman Proto, Siebe Gorman Savox, or Siebe Gorman Salvus.
An example of modern rebreather SCBAs would be the SEFA.
Rebreathers used underwater have the advantage of not releasing tell-tale bubbles, making it more difficult to detect divers involved in covert operations (see frogman). 
Breathing sets.
Frogmen's breathing sets on covert operations should have particular features.
Some are needed because they may need to swim fast and far.
Some are needed to avoid detection.
Sometimes patrol divers may have to be sent down to find or arrest submerged suspect divers.
For reasons stated in Anti-frogman techniques#Sending other frogmen against them, underwater fights between divers are much rarer in reality than in fiction, and thus suitability of the frogman's kit for "diver to diver combat" is less important than some other features when designing it; but the point is considered here for completeness.
USA frogmen's rebreathers tended to have the breathing bag on the back before enclosed backpack-box rebreathers became common. 
As a result, the frogman's breathing set should be fully closed circuit rebreather, preferably not semi-closed circuit and certainly not open-circuit scuba, because:  Open-circuit scuba makes large amounts of bubbles, showing where the diver is.
Open-circuit scuba makes noise (on exhalation, and regulator valve intake hiss as the diver breathes in) showing underwater listening devices where the diver is.
* There have been experiments with making released air or gas come out through a diffuser, to break the bubbles up; this may sometimes work with the small amounts of gas that are sometimes released by rebreathers, but open-circuit scuba releases so much gas at every breath that a diffuser large enough to handle it without making breathing difficult would be too bulky and would interfere with streamlining.
Holding the breath to avoid making noise at critical moments is not recommended and very risky: see diving hazards and precautions  The bulk of an open-circuit set makes the diver heavy and cumbersome in rolling over and changing course or speed.
The dive duration of open circuit sets is much shorter than the dive duration of naval rebreathers, in proportion to bulk.
However, some "technical diving" rebreathers are very burdened with safety devices such as inflatable flotation and open-circuit bailout.
(Some modern rebreathers, such as the Draeger, are lighter.)
The rebreathers which are the most compact in proportion to dive duration are oxygen rebreathers, but these are depth limited to about because of the oxygen toxicity risk.
The common sport open-circuit scuba set is not recommended for a fight against a trained naval or combat diver, because in any sort of underwater combat, a man with a large aqualung has a high rotation-inertia and is very unstreamlined in the twisting and turning involved in fighting and straight swimming, and his maneuvering is slowed critically compared to a man with a light streamlined rebreather with all parts close to his body.
Combat frogmen sometimes use open-circuit scuba sets during training and for operations where being detected or long distance swimming are not significant concerns.