If the districts had one thing in common, it was that no one was dancing in the streets. There was relief that something at last was about to move, but it takes more than Madeleine Albright playing what she fetchingly called an American "handmaiden" to disperse the suspicions of half a century. Jews and Arabs are still trying to fathom Israel's tenacious new Prime Minister, Ehud Barak.
"Every step is one-sided," grumbled Aharon Ringwald, locking his watchmaker's shop in Ben-Yehuda Street on the Jewish side of town. "It can only work to the Palestinians' advantage. They haven't kept any agreement they've signed, right from the beginning. They don't recognise our right to be in this land. They would still like to drive us out. And we're making it easier for them."
His neighbour, Herzl Muthada, had mixed feelings. "We give, but we don't get," he said outside his flower shop, overflowing with bronze, purple and white chrysanthemums, Michaelmas daisies and stately gladioli. "But it's too soon to know whether we're going to fare better under Barak. We have to wait - and give him credit."
Avi Ben, a wine merchant, had more faith in his Prime Minister. "Barak's done an excellent job," he argued. "He's playing tough, and it's working. It's the same in the way he handles his coalition. He's somebody with balls. It's important that he's strong, that he's a leader. That's how he has to be."
In Cafe Atara, the manageress, Yehudit Levisohn, was cautiously pleased with the deal. "We have to aim for peace," she insisted, "but I hope Barak will do it in the right way, even if it takes time." Two years ago, Ms Levisohn was wounded by a Hamas suicide bombing outside the cafe. "I'm sure," she added, "crazy people will continue to cause problems, but we mustn't let them succeed."
Yair Baruch, an 18-year-old waiting to start his three years' national service, had no reservations. "This agreement," he said, "is a good move for both sides. What's important is to create a better atmosphere. If there is an atmosphere of welcoming peace, that should work. The details are less important.
"Barak's already proving better than Bibi Netanyahu," he added. "Netanyahu wasn't consistent, so nobody trusted him. Barak is trying to do just the opposite."
Across town in Saladin Street, Wahib Tarazi, an Arab vet, was less confident. "At least we're getting something," he acknowledged. "But the Palestinian street won't be satisfied that they're only freeing 350 prisoners. It's ridiculous that we're making peace, and our prisoners are still in jail."
What did he make, I asked, of Mr Barak? "Netanyahu was better," he retorted. "He presented the real face of Israel. They want to take everything, but they don't want to deal with the Palestinians as human beings. Barak is more pragmatic. We all know how it's going to end. There'll be a Palestinian state. So why is he making it take so much longer than necessary?"
We met in a bookshop, where Mr Tarazi was looking for an Arabic-French dictionary. I asked the woman behind the counter, a Christian Arab with a cross hanging from her neck, what she thought of the peace agreement. "What peace?" she simpered. "What agreement?"