Remember Speedy, the little boy who visited in The Yellow Knight of Oz? Well, Thompson had to bring him back, right? Yep, and he got his own book in 1934 to boot!
Speedy in Oz opens with Umbrella Island, an island kept afloat in the sky by a giant magic umbrella, hitting Loxo the Giant in the head. He is so angry that he demands that in return, he be given a child of his choice to lace to his boots for him, and picks out a "boy" close to the king, who is named Sizzeroo. The people manage to convince Loxo to give them three months to prepare the "boy" for his future life, but it was actually Princess Gureeda who was selected. (The same style of clothing is worn by all inhabitants, which John R. Neill draws as resembling pajamas, though Thompson compares them to stereotypical Chinese garb; Gureeda also wears a single braid in her hair, like men on Umbrella Island usually do.)
Over in the Great Outside World, Speedy, a former visitor to Oz, is helping his Uncle Billy in his work at an excavation dig, when they get to a complete dinosaur skeleton. Speedy convinces his uncle to put it together, but shortly afterward, a geyser erupts, carrying Speedy and the skeleton high into the air. At the same time, the dinosaur's bones are fused together, and it comes to life. Able to speak English, Speedy names it Terrybubble (when he mispronounces "terrible"), and Terrybubble manages to keep Speedy in his chest, and they land on Umbrella Island.
When one the King's advisers sees Speedy, he suggests that Speedy be given to Loxo instead of Gureeda, but Speedy finds a friend in Waddy, the Wizard of Umbrella Island, who makes him his apprentice. When Umbrella Island crash lands in between two warring islands, it is Speedy who saves the island from destruction by a water cannon that can sink islands.
Terrybubble overhears the plan to give Speedy to Loxo, so he takes both Speedy and Gureeda to Oz, unwittingly bringing them straight to Loxo's cave. When Waddy discovers the disappearance, they head to Oz to enlist Ozma's help. She, the Wizard, and the Scarecrow devise a solution that works best for everyone. They trick Loxo into eating a cake that makes him shrink to a human size. In a surprising turn for a Thompson villain, he decides to live peacefully from then on. (After all, he can lace his own boots now.)
Speedy returns home, but Waddy misses his apprentice, and Thompson says she feels sure that Speedy will one day return to Umbrella Island and marry Gureeda and become the next king. (A story she never told.)
Thompson said Speedy in Oz was her favorite of her Oz books. For me, it's not hard to see why. It boasts one of the tightest plots of her books. There are no extra countries the characters visit that do not play a role in the story. And there's no contradictions with Baum as his characters aren't used very much.
So, if there's one Thompson book you ever read, I heartily recommend Speedy in Oz.