Are you sure that you learn compounds in volume III? That's a book description which doesn't mention anything about them: " [...] goes beyond the general-use kanji treated in the previous volumes to bring the student to the level of proficiency of the university graduate - roughly 3,000 kanji. The work falls into two parts. Part I introductes the meaning and writing of the kanji; Part II, the readings."
I just looked for book three online, and it looks like the book is no longer in print. While book one has you learn the meaning, book two has you learn (primarily) the On reading of each character. Finally, in book three, you (used to be able to) learn more advanced techniques of reading kanji in context; that is, reading essays, newspaper articles, etc.
Even without book three, though, if you take what you've learned from books one and two and tackle a Japanese text (manga, novel, newspaper, etc.), then you'll be able to identify the meaning and reading of the majority of the kanji you will come across.
This is more than half the battle.
Combining kanji you already know to form vocab you are learning (or better yet - have already learned) is much, much easier than trying to learn a word AND the kanji AND the reading of the kanji AND the stroke order of the kanji AND....
Get what I mean?