In "Dr. Strangelove", a significant chunk of drama happens inside a B-52 flying fortress on a doomsday mission. Whereas the satirical elements are all there -- the pathetically patriotic pilot played by Slim Pickens and the screwy "Plan R" he is given, Kubrick decided to play it straight, as in he did not spare any mundane working detail of a long-range bomber with the sole mission of carrying a hefty atomic payload and releasing it on the "evil" Soviet empire. Consequently we get to see a lot of close-ups of switches being flipped on the plane's instrument panel, and the pilots' nonchalance while reading aloud the "manual" of an atomic first strike. Despite the abundant hilarious materials, the solemnity of the subject matter is as sharp as the black-and-white photography Kubrick opted to use for this anti-nuke satire.
Anyone who has tried to create a satirical piece, either literarily or cinematically, knows that the tricky part is knowing "how much is too much". Kubrick could choose to let Peter Sellers go bananas with the Dr. Strangelove character, yet, wisely he did not. His keen dramatic instinct is evident in the way he reined in the performances of Peter Sellers, Sterling Hayden, George C, Scott, et all. A director of lower caliber would probably have no control over these brilliant actors, because they could theoretically go in every direction and still be funny in a comedic sense, but not necessarily in a message-pounding satirical sense.
A bonanza of trivia about this beloved 1963 black comedy can be found on imdb.com. Do you know that Peter Sellers was supposed to play four roles, including Major Kong? But Sellers reportedly had a problem developing a Texas accent, so the production team approached John Wayne who didn't even get back to them (wonder why?). Eventually they settled on Slim Pickens, who worked out perfectly.