"You have a beautiful gin martini ruined by some cheap olives, " Mr. Palazzi says.

WSJ: Will Lyons on Wine: Ginning Up on Classic Cocktails

"In the '80s, drinks culture became a little bit cheesy, " says Mr. Palazzi.

WSJ: Will Lyons on Wine: Ginning Up on Classic Cocktails

The charming Mr. Palazzi took a break from greeting his guests in the comfortably crowded bar to thank Fleming for his part in Duke's success.

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"If you look along the way, there are many palazzi that are cracked, walls have fallen in on some of them, " he said.

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So vodka stuck, but in Mr. Palazzi's opinion, the best martinis are always made with gin, as it adds a little more complexity and flavor.

WSJ: Will Lyons on Wine: Ginning Up on Classic Cocktails

According to the bar's current manager, Allesandro Palazzi, shaking or stirring with ice is not needed (nor desired, as it dilutes the drink) when you freeze the main ingredients.

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Once in Naples, Caravaggio fitted in like a native, embracing the metropolis that was three times the size of Rome, riven by extremes of wealth and poverty, light and dark, palazzi and shantytowns.

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"Martini is the purest cocktail, " says Mr. Palazzi.

WSJ: Will Lyons on Wine: Ginning Up on Classic Cocktails