The necessary act is farmed out or delegated to a third party ostensibly unconnected with the major player. This can take the form of a private person or mercenary being hired to carry out a task, or a government or agency being asked or compelled to do you a quiet favor.
One problem with being "deniable" is that not only are you on your own if you get in trouble, but your own employer has a positive motive to betray you to prevent you from talking about your actions on their behalf.
One way of concealing sources and methods is to use deniable assets on your behalf. The assets use different techniques than your own, and while their actions may be motivated by information from your sources, you have the chance to sanitize any information before you give it to them.
In fiction, the Mission: Impossible team was deniable, as "the Secretary will disavow any knowledge of your actions if you are caught or killed." (Also mention the novels Crisis Four, etc. about fictional operative Nick Stone sp? and mention author and background, about a deniable "K" operatior for British Intelligence.)
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