Mr Hoppy is an lonely old man with two passions. The first is his garden, situated on his balcony on the second floor, and the second is the old lady who lives below him. The balcony of Mrs Silver is larger than that of Mr Hoppy. From time to time Mr Hoppy leans over his balcony to enter into conversation with her, but she has no idea that Mr Hoppy has fallen in love with her because she has only eyes for her tortoise Alfie.
Alfie lives on the balcony all year round, hibernating in his little house during winter. Every year Mrs Silver weighs Alfie, and every year he weighs 13 ounces. One morning Mrs Silver and Mr Hoppy are chatting and Mrs Silver expresses her concerns that Alfie has only put on three ounces during all the years she has had him. She feels sorry for Alfie because the other tortoises have grown up much bigger, and she thinks that Alfie might be jealous of them - but Mr Hoppy is jealous of Alfie!
Mr Hoppy conceives a plan to win Mrs Silver's heart. He tells her that he knows a secret to make tortoises grow. He hangs down a piece of paper with magic words written upon it, which Mrs Silver must chant at Alfie three times a day. In reality, the magic words are merely ordinary words written backwarsd. When Mrs Silver demands to know what the words mean, Mr Hoppy explains that tortoises are backwards animals, so they only listen to words spoken backwards.
Mr Hoppy visits shops across the whole town to buy variously sized tortoises. Then, to construct a crane to take hold of the tortoises, he goes to the mechanic's shop where he had worked.
While Mrs Silver is at work, Mr Hoppy exchanges the tortoise for another which weighs exactly 2 ounces more. Mrs Silver doesn't notice the difference upon her return, but continues to utter the magic words.
For the 8 following weeks, Mr Hoppy leans over his balcony with his crane to exchange "Alfie" with another slightly larger tortoise. With a weight of 27 ounces, the last tortoise is too big to get into Mr Hoppy's house, and Mrs Silver finally notices the difference. She is so happy that she invites Mr Hoppy to her apartment to hold "Alfie".
Mrs Silver now wants Alfie to be a little smaller because she doesn't want to make a bigger opening for his house. Mr Hoppy gives her some new magic words, and Mrs Silver agrees to try them for a day. After several attempts, Mr Hoppy exchanges "Alfie" with a tortoise that goes perfectly through the house's door.
Mrs Silver is so delighted with Alfie's response that she invites Mr Hoppy over for a cup of tea. He finally plucks up the courage to ask Mrs Silver to marry him, and she accepts him.
Mr Hoppy takes all his superfluous tortoises and gives them away free of charge. A little girl, Roberta Squibb, adopts the original Alfie, and he lives happily in his garden. After Alfie reaches 30, his size finally doubles.