WATCH: John Oliver starts his Daily Show run with a hit on the NSA

John Oliver kicks off his summer run hosting The Daily Show by acknowledging what many fans of the show are probably thinking: It's weird to see him sitting at Jon Stewart's desk. He reads a welcome note from Stewart promising him that no big news ever breaks in the summer — cueing up the topic of his monologue: The new series of big leaks on the National Security Agency's surveillance reach.

Or, as he calls the segment: "Good news! You're not paranoid."

Almost immediately, Oliver shows that "Jon Stewart left The Daily Show in good hands," says Tim Molloy at The Wrap. It took Oliver "about 90 seconds to find his stride," and his "jokes only got more blistering as he moved" from relatively benign jokes to the "legitimate target of mockery, the federal government."

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Oliver gets in some clever riffs about the PRISM logo looking like a "Chinese bootleg of a Pink Floyd album," how leaker Edward Snowden's brags of unfettered wiretapping ability remind him of "every conversation I've ever had with an IT guy," and how the FISA court's rubber-stamp is like having American Idol "with four Randy Jacksons."

All this sets up Oliver's best joke. Thanks to Snowden's whistle-blowing, he says, we now know that the NSA routinely collects an unprecedented amount of information about "that small, select group of us who either make phone calls or use the internet." Given this level of scrutiny, "I bet the Amish are feeling pretty f--king smug right now," Oliver says — or at least "they would be feeling that way if they had any idea that this story was happening."

The topic of what tradeoffs we're willing to make between security and privacy is a serious one, and Oliver ends his monologue on a serious note. Responding to President Obama's assertion that the NSA programs have a whole range of safeguards and congressional oversight, Oliver says:

Criticizing his host government on his maiden voyage was a little risky, but the audience ate it up, says The Wrap's Malloy. That's in part because Oliver's "Britishness, which we Americans oddly interpret as politeness, allows him to get away with being more aggressive than Stewart."

No, "Americans love it when British people criticize us," period, says Melissa Maerz at Entertainment Weekly. So maybe this summer hosting gig will work out for The Daily Show, after all. Oliver "worked in a few good jokes," of course, but his best moment came in the end, "from just telling the truth — which is, when you think about it, what most great comedy boils down to."

The next part — a return to comedy — is pretty great, too, though. Oliver talks to the full roster of Daily Show correspondents, ostensibly about the NSA leaks, but it gets pretty personal pretty quick. Watch: