I’ve said this before, but it bears repeating: Sandra Bullock is best known as a comic actress, but her best work tends to come in roles where she isn’t concentrating on being cute and lovable. In movies as different as While You Were Sleeping, Murder by Numbers, and 28 Days, her portrayals of essentially lonely characters bring out a haunted, melancholy streak in her that renders her much more interesting than she is in, say, Miss Congeniality. That same quality is starkly in evidence in The Lake House, a movie that really shouldn’t work as well as it does.

She plays a Chicago hospital physician named Kate who prepares to move out of the eye-popping modernist lake house she’s been living in by leaving a note in the mailbox for the next tenant, asking to forward her mail. The note is picked up by architect-turned-real estate developer Alex (Keanu Reeves) on the same date two years earlier, in 2004. He writes back to her, expressing puzzlement as to how she knows things about the house that haven’t happened yet. Once they conquer their disbelief over how they’ve broken the time-space continuum, they fall in love as they write lengthy letters to each other. (Why do they never think of e-mailing?)

The movie is based on a 2000 Korean film that played at festivals in this country under the title of Il Mare, which I must admit I haven’t seen. Screenwriter David Auburn (Proof) does the adapting, and his script is intelligent and graceful, though lacking in humor and riddled with small misjudgments — Alex’s description of the lake house as “seductive” is wrong. With Alex and Kate indulging in involved conversations, you sense that this would work even better on the stage.

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Veteran Argentinian filmmaker Alejandro Agresti, in his first Hollywood effort, ensures that it works on the screen. His last movie was the intensely annoying comedy Valentín, but here he dispenses with that film’s cloying sentimentality in favor of a lyrical simplicity that befits the material. When Alex sends Kate on a walking architectural tour of Chicago, Agresti captures the city’s buildings in their breathtaking beauty. He also gives himself an amusing wordless cameo as a guy sitting next to Kate on the El.

As is usually the case with romantic films, however, everything relies on the two actors, and they deliver, whether it’s Reeves in an unexpectedly moving sequence after the death of his emotionally distant starchitect dad or Bullock in an extreme close-up, her eyes widening with grief when Kate finds out why she can’t find Alex in 2006. (The movie sort of gives away his fate early on but then goes back on it, a move that doesn’t entirely work. Check out Brad Anderson’s 2001 film Happy Accidents for a romance with a weirder time-travel gimmick that handles everything better.) The two actors are especially good in the movie’s fulcrum point, a long exchange between Alex and Kate when they meet face to face in 2004, before she knows who he is. The quiet remarkability of this scene is everything you’d wish for, as Alex draws out Kate on why she pushes away emotional involvements, and it’s emblematic of the strength of a movie that turns out as a most unlikely success.

 The Lake House
Starring Keanu Reeves and Sandra Bullock. Directed by Alejandro Agresti. Written by David Auburn, based on Kim Eun-jeong and Yeo Ji-na’s screenplay. Rated PG-13.