We tend to group the mystery and the thriller together, but as The Best Offer shows you can cleave some separation between the two. Starring Geoffrey Rush as an eccentric auctioneer who falls for a much younger heiress suffering from agoraphobia, the film unfolds in those two distinct parts -- mystery and then thriller -- and suffers for it.

The Italian film, which is written and directed by Giuseppe Tornatore, works as a riddle. Rush's character, Virgil Oldman, is an exceedingly private crank and a germophobe. But he also has the keenest of eyes for fine antiquities, finding priceless pieces of art hidden beneath cobwebs or face down on the floor of an attic or basement. It's a talent that makes him a hot commodity as an appraiser and auctioneer. It's also one that leaves him susceptible to malfeasance.

With his unparalleled eye winning him the blanket trust of his clients, Oldman purposely passes off select pieces of his clients' art as forgeries then purchases them at his own auctions through a proxy, Billy, who is played by Donald Sutherland. All of the pieces are portraits of women, and all of them are stored in a hidden room in his apartment.

That's as good a place as any to talk about the young heiress who dramatically disrupts his routine. Claire, who is played by Sylvia Hoeks, hires Virgil to work on her parents' estate, but her agoraphobia is so extreme that she's unwilling to even meet face-to-face with the man in her employ. This exasperates Virgil, but also leaves him with an insatiable curiosity about his client that accelerates with each strained conversation, either over the phone or through the wall that separates her private quarters from the rest of her parents' villa.

For a lifelong bachelor and virgin who has trouble relating to women, there's an obvious symmetry to the scores of portraits in his safe room and his budding relationship with Claire as it progresses painstakingly from business only to friendship to romance. Even for a man who regularly swindles the people he works for and who is stealing pieces of a priceless automaton from among Claire's belongings, the lonely Virgil is a sympathetic character. He can count only two friends, Billy and an artificer, Robert, played by Jim Sturgess, who lends him romantic advice and helps assemble the automaton part by part. As such, Claire's ability to break through her counterpart's stuffy and staid exterior is as intriguing as the source of her debilitating fear.

As long as The Best Offer is this space, it works well enough. It's nice, too, to see Rush playing something that's a far cry from Captain Barbossa. The problem is the jarring shift in the third act that turns the film from a slow-burn mystery in to a tortured and overly elaborate caper movie. Yes, there's a major twist. All is not as it seems. The film rushes to explain every part of the twist it can, but it doesn't really stand up to even the superficial application of scrutiny.

The sloppy conclusion didn't bother me so much as the wasted opportunity of further exploring everything as it was before the big, dramatic reveal. Virgil Oldman is an interesting character. So too is the woman who captured his attention. It's disappointing that Tornatore didn't agree enough to follow this odd couple a little farther down the road.