Our current location is luxurious, far from the squalid Havana of the Conde books, with its crumbling houses, broken-down lifts and dirty streets. The restaurant is called Divino, and is one of the privately owned eateries, of varying quality, that have mushroomed in Cuba lately, especially under the US's now-partially reversed detente and President Raúl Castro's also-stalled reform drive.
This one has red tablecloths, uniformed waiters and a terraced view of lush grounds. It even has a wine cellar. I suspect it is not Padura's first choice - although it is near-deserted tonight and therefore discreet - nor would it be Conde's. The detective often criticises the luxury and shine of easy money you sometimes see in modern Cuba. Is that well-off stranger an entrepreneur done good, or only an apparatchik with connections? Few things are what they first seem.
Padura's latest book, The Transparency of Time, to be published in January, develops the theme of Cuba's widening social divisions. It sees Conde chasing a stolen 13th-century statuette of a black Virgin Mary, and takes him from Havana's poorest corners to its richest - "much more luxurious than here", he says with a sweep of his hand. The book "explores the relationship between man and history . . . how man is formed by history, and malformed". He grimaces.
A bow-tied waiter arrives, and uncorks the first of two bottles of red wine I have brought with me from Miami. We declare it delicious. Padura gets cigarettes from his utility belt; I follow suit. "Oh good," he says. We smoke and examine the menus with care.
Eating has an important place in Padura's books. This is not because of hunger per se - "Cuba is probably the only Latin American country where nobody dies of hunger" - but rather because of the perennial uncertainty of when or what Cubans will eat next. This neurosis is born of decades of rationing, empty supermarket shelves, and the dismally frequent response when searching for basic goods: "No hay" - there isn't any.
"Conde and his friends call it the 'camel philosophy'," Padura says. "If you invite Cubans to eat at a restaurant like this, and ask them what they think of the food, they usually don't reply 'good' or 'bad' but how much they ate. A judgment of quality is swapped for quantity." It's a characteristic Padura comment: precise and fully formed, critical yet respectful.
We opt for plenty, too. For the centre of the table we order tostones, the fried green plantains that are a Caribbean staple, a mixed salad, and dishes of white rice and black beans. For a main course, Leonardo orders grilled chicken. I choose roast rabbit.
Padura's journey from a peripheral Havana neighbourhood to global stardom is remarkable. He and his wife Lucía, 58 - to whom he dedicates all his books and who collaborates on his film scripts - are both members of what he has called the "gullible generation". They came of age with the revolution, believing in Fidel's vision of a socialist future that dogma assured them would arrive.
His father, the owner of a small shop, was a Mason, and his mother a Catholic. Both inculcated Padura with important ethical principles, but "I grew up far from the world of books", he says. He wanted to study journalism, but instead read philology at the University of Havana. He worked briefly as a journalist at Juventud Rebelde, the communist youth paper, and reported on the war in Angola.
His break - wrong to call it lucky - came after the fall of the Berlin Wall, when Cuba was plunged into the so-called "Special Period" of the 1990s, a time of economic crisis and extreme rationing. Padura was made editor of a magazine that stopped publishing during the crisis, a situation that left him with a modest salary but no real work. Instead, he wrote.
His first Conde book was published abroad in 1991, after rejection at home. His second, published in 1994, won a national prize. Words poured out of him - novels, screenplays, journalism, and a semi-fictional life of José María Heredia, the romantic Cuban poet.
He won international literary prizes, most helpfully, in 1995, from the Café Gijón in Madrid. With its $16,000 prize - a fortune in Cuba, given the average state wage of $20 a month - Padura bought his car.
"I may not be the best Cuban writer of my generation, but I am the hardest-working," Padura says. "When we got back from Spain this week from a literary festival, we arrived at 11pm. At 5am, I was back at work. I am obsessive."
The comment summons an image of Padura as a tireless tropical Hephaestus hammering-out literary filigree in his study above the garage.