"Fifties music backs the cheery efforts of Pilot Uniqua to deliver singing telegrams to a grumpy pirate, a peace-loving queen, and even the Abominable Snowman!"
Uniqua is in the backyard, pretending to soar like an airplane. She comes to a halt and introduces herself to the viewer as Pilot Uniqua, an airplane pilot. She explains how she flies around the world delivering "singing telegrams" to make grumpy people smile. She sings "A Singing Telegram" as the backyard transforms into an airport.
Uniqua hops into a pink 1930s plane. A printer located inside the plane prints out a picture of a blue penguin pirate. Uniqua tells the viewer that she needs to go to Pirate Captain Moody's ship to deliver a singing telegram to him. She flies off. Meanwhile, at the ship, Captain Moody is mopping the deck of the boat. He sings "Clean, Clean, Clean" as he explains that he will never rest until his ship is clean.
Uniqua lands on the boat and exits her plane. Her foot gets stuck in a bucket, and its contents are spilt when she pulls her foot out. Then she leaves watery footprints on the ship's floor. Moody greets her with yelling and screaming, because she just made a mess on Moody's boat. The captain yells at her to get off the deck and Uniqua jumps on to the ship's mast. Pirate Moody demands her to get off the mast. She runs down and climbs up on to the sail. She slides down as Moody yells to her that he just ironed the sail.
Pirate Captain Moody makes her walk the plank. Uniqua gets out a harmonica and begins singing "A Singing Telegram". Moody tells her to stay right there on the plank (to get his harmonica and sing along) but Uniqua gets the impression that he disliked her song. She runs away back into her plane and flies away as Moody comes back screaming.
The printer inside the plane prints out another picture, this time of an Indian Maharani. Uniqua knows that it is a new telegram and Maharani Tasha. So she flies to India. Meanwhile, at Tasha's palace, the Maharani is relaxing on her couch. Birds tweet outside, causing Tasha to walk over to her window and tell them to be quiet. The birds continue chirping. Tasha tells them to be quiet again, and the birds do not follow. Tasha yells to them to be quiet immediately and they stop.
Uniqua lands near the palace noisily, causing Tasha to wonder about what made the loud sounds. Uniqua enters the building quietly and then yells "SURPRISE!", causing the Maharani to scream. Pillars fall like dominoes, causing a giant gong to crash and destroy Tasha's couch. Maharani Tasha is so mad at Uniqua for make too much noise, so she pulls a lever. Tiles on the floor move away, revealing a pit. Tasha tells Uniqua that she has to stay in her Chamber of Silence forever to pay the price of make too much noise. Uniqua quickly sings "A Singing Telegram". Tasha tells Uniqua to stay right there (so Tasha can get a harmonica), but Uniqua thinks Tasha disliked the song.
Uniqua runs outside, but Captain Moody has caught up with her. Moody yells and is followed by Tasha yelling angrily. Uniqua sneaks out of the argument and flies off. The two grumps shake their fists at Uniqua madly. They sing "A Grump Like You" as they meet each other. Then they head to wherever Uniqua is going.
Meanwhile, the printer in Uniqua's plane prints out a picture of the Abominable Snowman. Uniqua flies to a snowy mountain. Tyrone the Abominable Snowman has just finished shoveling a long, long path leading to his cave. Then Uniqua's plane comes and knocks lots of snow on to his path. The Abominable Snowman is so mad at Uniqua when she gets out. The snowman chases Uniqua angrily, screaming "Grr!" madly. Uniqua screams and runs to her plane. She climbs on top of it and sings a quick version of "A Singing Telegram". The Abominable Snowman tells Uniqua to stay right there (to get his harmonica), but Uniqua thinks the Abominable Snowman disliked like her song so she flies back to the airport. Tasha and Moody arrive on a sled and begin shaking their fists at Uniqua. The Abominable Snowman is confused because everything is happening so fast, but goes along with it by shaking his fist as well.
Uniqua arrives at the airport and sadly tells herself that "maybe singing telegrams aren't so swell after all". Then the three grumps run up to her, screaming. Uniqua screams again, but the trio of mad people sing "Thank You" to thank her for the songs. Uniqua accepts their apologies. Tyrone's stomach growls and he invites them to his house for pudding as the landscape transforms back into the backyard. They sing the end song and enter Tyrone's house. Uniqua opens the previously closed door and shouts, "Mi-mi-mi-mi-mi!"