A Mrs Ernestine Todd, from Clapham, asks Poirot to help her find her cook, Eliza, who has disappeared. Poirot, who aims to accept only really significant cases, is at first insulted by such a trivial request. However, after he sees the contents of the missing cook's trunk, he decides the case could prove to be worthy of his talents.

Within hours of the Bonfire Night fireworks beginning Poirot finds himself investigating a violent death in Hastings' mews garage.

Poirot discovers a murder in his own block of flats, and goes on the trail of boisterous neighbours and strange nocturnal noises in the lift shaft.

Lord Mayfield, an aircraft manufacturer, tries to trap a spy at his country house, but his plan goes terribly wrong. Lady Mayfield sends for Poirot, who tells a few home truths.

Millionaire business man Benedict Farley, a well known eccentric, consults Poirot about bad dreams he has been having. Mr. Farley has dreamed repeatedly of killing himself. Sadly, he does not follow Poirot's advice. When Farley is found dead, Poirot fails to believe that it is suicide and suspects a murder plot relying on hypnosis.

Poirot calls to see the veiled lady of the title (Lady Millicent Castle-Vaughn) at her London hotel. Lady Millicent is about to be married, but a mean blackmailer called Lavington has got hold of a love letter she wrote years before to another man. Lavington wants twenty thousand pounds, and Poirot makes up his mind to recover the letter himself, even if it means impersonating a Swiss locksmith.

Hastings and Poirot are playing Monopoly when they are interrupted by Lord Pearson, the elegant Chairman of the London and Shanghai Bank. The banker asks them to investigate the disappearance of a Mr Ling - a highly-valued customer who before he went missing had arranged to sell Lord Pearson a map showing the location of a long-lost silver mine. Ling is found murdered, a young stockbroker is implicated, and Poirot has to untangle a complicated plot.

Poirot travels to Cornwall, summoned by a Mrs Pengelley, who suspects her dentist husband is poisoning her because he's fallen in love with his young assistant. Unhappily, Poirot finds Mrs Pengelley dead on his arrival, so he sets out to catch her killer.

Poirot's Christmas is interrupted by Simeon Lee, who believes his life is threatened. Simeon is soon killed and his diamonds stolen.

Poirot and Hastings are at Lake Windermere for an attempt on the world speed-boat record. An elderly widow is hurt by falling down stairs, then later killed by poisoning with phosphorus.