MIAMI — Some of the thorniest conversations in the long road toward full relations between Cuba and the United States have only just begun in recent days: The two sides are sitting down for the first time to discuss the American properties Cuba confiscated decades ago.

The very idea of compensation for property and businesses seized in the wake of the Cuban revolution sent a quiver of excitement down the backs of the thousands of people who lost everything from sugar mills to family homes to oil refineries.

People started dusting off yellowing deeds. Lawyers were called.

But what if Cuba approaches these historic talks with a rather different unsettled claim in mind?

In 1999, a Cuban court found the United States government liable for deaths and damages caused by America’s “aggressive policies” against the island — namely, the Bay of Pigs invasion and the trade embargo prohibiting American citizens and companies from doing business in Cuba.