It is over another breakfast that he discovers another muse, Alma (Vicky Krieps), who waits on his table at a hotel restaurant. She is of indeterminate non-British origin—the actress herself is from Luxembourg—and Reynolds finds himself intrigued. He asks her to dinner, where he promptly blots off her lipstick so he can better “see” her. Romantic? Possibly. Controlling? Without question.

Like those who came before her, Alma is soon ensconced in Reynolds’s home-cum-dress-shop, where she exists in large part to allow him to perfect her, Pygmalion-like. Unlike Henry Higgins, however, his goals are not phonetic but sartorial. As he fits her for one particular dress, he remarks that she has “no breasts,” before adding, “Oh no, you’re perfect. It’s my job to give you some. If I choose to.”

The relationship is an odd one. Though it is surely sexual, such activities take place behind closed doors. And sex is, in any case, a secondary concern. Where some men desire most to undress women, Reynolds desires most to dress them. Alma is, for him, essentially a mannequin that talks.

But she is also—and in this regard we sense that she differs from her predecessors—a mannequin that talks back. At times subtly and at times directly, she tries to break out of the role Reynolds has assigned her. The odds are clearly stacked against her: He has wealth and fame and Cyril (whom he refers to as “my old so-and-so”) on his side. Alma, for her part, has merely Reynolds’s presumably temporary infatuation and her own unexpectedly steely will. They ultimately take her farther than you might imagine.

Anderson directs with an understated elegance worthy of the House of Woodcock. He has described the film as a “Gothic romance” inspired by Rebecca, and he ratchets the tension with Hitchcockian precision, especially as the plot’s twists begin to reveal themselves. Alas, as has occasionally been the case in the past—notably in another flawed near-masterpiece, Magnolia—Anderson allows certain storylines to dangle awkwardly. One of these is the element that gives Phantom Thread its title: Reynolds’s habit of sewing secret talismans into his clothing—a lock of hair here, a secret message there. It’s a fascinating idea, never fully explored. A phantom limb, perhaps? Or a loose thread?

Day-Lewis’s performance at times recalls his turn as Newland Archer in The Age of Innocence. Apart from the periodic outburst—as when a wealthy woman has the effrontery to fall asleep in public while wearing one of Reynolds’s dresses—powerful feelings are expressed in muted tones. Yet unlike Newland, Reynolds has a ferocity beneath his studied exterior. He is both fueled and intermittently felled by his own perfectionism. Exhausted after a show, he grows ill and is tended to by Alma, who finds him “very tender, very open” until he regains his health and can return both to work and to his customary demeanor.