And, again improbably, the American story line is the strength of “Zerozerozero” — when it’s onscreen, there’s more to watch than a coolly efficient international crime thriller. Perhaps because they couldn’t fall back as easily on mafia or narco clichés, Sollima and his collaborators came up with a framework for the American family — domineering father, children struggling to prove themselves in the business, sister fiercely protective of brother with degenerative disease — that’s usefully melodramatic and gives Riseborough and DeHaan room to portray a real and subtly moving relationship.

Their scenes, as the sister and brother tend to the shipment through increasingly dangerous and implausible complications on the Atlantic and in Africa, provide emotional and dramatic jolts in what’s otherwise a polished, visually absorbing, highly engineered prestige-TV package. Locations in northern Mexico, southern Italy and the Sahara are photographed in ways that are simultaneously arresting and unsurprising, and the “Gomorrah”-like ambience — violent action depicted with a melancholy austerity of tone and style — is reinforced by the incantatory music of the Scottish band Mogwai.

That kind of package is an impressive thing in its own right, and the Italian sequences have their share of coups, like an opening scene in which the gangster emerges from a cramped, windowless cell into a wild mountain landscape. But “Zerozerozero” also has stretches, especially in the Mexican story line, that serve mostly to fill our expectations of this kind of show, sequences in which the narco-thriller conventions are just there for their own sake. As a globe-spanning attempt to tell a start-to-finish story of the drug trade, “Zerozerozero” evokes Steven Soderbergh’s 2000 film “Traffic” (based on the superior British mini-series “Traffik”), and it shares the movie’s tendency to sacrifice dramatic specificity for the sake of broad-brush platitudes.

It has a saving grace, though, in Riseborough, who overcomes an attention-grabbing hairdo — a two-tone affair resembling an alien warrior’s helmet — and makes human and disarmingly charming what could have been a flat, cartoonish character. Spoiler alert: Her character, unlike many, survives, and the smile that pops onto her face amid the carnage of the show’s final scene is enough to make you hope for a second season.