"The only thing I understand is that Rouhani's language is respectful, while Ahmadinejad's was not," said Hasan Makani, a 42-year-old construction worker. "I'm not familiar with politics, but I hope things will improve under Rouhani."
Iran, though, has been here before in some ways.
Reform-minded President Mohammad Khatami took office in 1997 with similar expectations of a thaw with Washington and rolling back the hard-liners' influence. But Khatami was slapped down hard by his conservative opponents, who helped usher in Ahmadinejad as his successor.
Rouhani has much greater pressures at home and abroad. He must revive nuclear talks with world powers and persuade the U.S. and allies that easing sanctions will reap rewards with still-unclear Iranian concessions. The Revolutionary Guard is also a potential spoiler if it sees Rouhani going too far, too fast even with the apparent backing of Iran's Supreme Leader Ayatollah Ali Khamenei.
The Guard is the only institution capable of standing up and pushing to reverse course. Without Khamenei, the legitimacy of Rouhani's overtures to Washington would be severely undermined.
Already, the Guard seems uneasy in the unfamiliar spot of bystander. Khamenei has lectured Guard commanders on staying out of politics, saying it was a time of "heroic flexibility" in policymaking. He also allowed Rouhani to name his U.S.-educated foreign minister to head the nuclear talks, taking it out of the hands of security officials.
In response, the Guard warned Rouhani about reaching too far. The Guard-linked Fars news agency even quibbled with the translation of CNN's interview with Rouhani in which he called the Holocaust "reprehensible."
"Heroic flexibility does not include passivity or surrender," said the Guard's acting commander, Hossein Salami.
On Thursday, a senior official in the Guard's elite Quds Force, Ghassem Soleimani, interpreted President Barack Obama's declaration that the U.S. doesn't seek "regime change" as a sign of Washington's weakness, not an offer of outreach.
"This is not a favor; this is an announcement of inability," the semiofficial Fars news agency quoted him as saying.
Many Iranians are basking in the positive vibes after eight years of barbs from Ahmadinejad, who once called U.N. Security Council resolutions as worthless as "used tissue."
Tehran resident Ziba Seddighi gushed over the "beautiful dialogue" set in motion by Rouhani, who used a U.N. General Assembly speech Tuesday to promote "hope, rationality and moderation," yet also chided the U.S. and other Western powers for dividing the world in "superior us and inferior others."
In a middle-class neighborhood, stay-at-home mother Fatemeh Mahmoudi was happy Rouhani and Obama traded words of goodwill at the U.N., but did not shake hands, because such a gesture could create too much blow back at home from hard-liners.
Shrugged 29-year-old construction worker Hasan Assadi: "I would have liked him to shake hands, but this is not the end of the world. Maybe next time."
Those in business look mostly to Rouhani's appeals to ease Western sanctions, which include measures that have bumped Iran from international banking networks and dealt a sharp blow to trade.
One barometer of street sentiment is the value of the national currency, the rial, which plunged late last year amid sanctions and fears of possible military action over Iran's nuclear program. The West believes Iran could eventually produce nuclear weapons. Tehran insists it only seeks reactors for energy and medical use.
The rial selling for more than 40,000 to the U.S. dollar earlier this year has stabilized around 30,000.
"Sanctions remain in place. Nothing has changed on the ground, but the biggest change so far has been revival of hope," said Bita Nazari, a young woman with purple nails Rouhani's campaign color. "The ice cannot be melted overnight."
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Associated Press writer Nasser Karimi contributed to this report.
