Isaac,
I, too, am a bit confused by what you mean by 'compounds'. Do you mean words that are made up of two characters? In Chinese there are plenty of words that are one-character as well as plenty that are two-character. Look at this example.
我不会说中文。I can't speak Chinese.
Note the number of characters for each English word.
我 = I (one-character)
不会 = cannot (two-character)
说 = speak (one-character)
中文 = Chinese language (two-character)
Or do you mean the 'pieces' (the 'radicals') that make up individual characters? Look at these three characters:
仙、付、休
Look at the left side of each character. All three characters contain the radical for 'human being' on the left side.