Here is a tantalizing puzzle, wrapped in eroticism and presented with the utmost elegance. It seems to be telling us a very simple story in a straightforward way, but you might need hours to discuss it with your friends before you know (if then you do) exactly what happened. The film takes place in the 1694 English countryside. A rich lady (Suzman) hires an itinerant artist to make 12 detailed drawings of her house. He (Higgins) strikes a hard bargain. In addition to his modest payment, he demands "the unrestricted freedom of her most intimate hospitality." Since the gentleman of the house is away on business, the lady agrees, and thus begins a pleasant regime divided between the easel and the boudoir.

All of this is told in the most precise way. All the characters speak in complete, elegant, literary sentences. All the camera strategies are formal and mannered. The movie advances with the grace and precision of a well-behaved novel. There is even a moment, perhaps, when we grow restless at the film's deliberate pace. But then, if we are sharp, we begin to realize that strange things are happening under our very noses.

The draughtsman demands perfection. There must be no change, from day to day, in the view he paints. He aims for complete realism. But little changes do creep in. A window is left open. A ladder is found standing against a wall. There are things on the lawn that should not be. The lady's daughter calls on the artist to suggest that a plot might be under way, and that her father, the lord of the manor, might have been murdered, and that the artist might be about to be framed for the crime. As payment for her friendship, the daughter demands the same payment in "intimate hospitality" as her mother. Now the artist is not only draughtsman but lover to mother and daughter, and the possible object of a plot to frame him with murder.

There's a lot more, all unfolding at the same deliberate pace. A mysterious statue appears in the garden, as does an eavesdropper, and misbehaving sheep. The story could have been fashioned into a bawdy romp like "Tom Jones." But the director, Peter Greenaway, has made a canny choice. Instead of showing us everything, and explaining everything, he gives us the clues and allows us to draw our own conclusions. His movie is like a crossword puzzle for the senses.