  We use a novel decomposition to create succinct data structures -- supporting
a wide range of operations on static trees in constant time -- for a variety
tree classes, extending results of Munro, Nicholson, Benkner, and Wild.
Motivated by the class of AVL trees, we further derive asymptotics for the
information-theoretic lower bound on the number of bits needed to store tree
classes whose generating functions satisfy certain functional equations. In
particular, we prove that AVL trees require approximately $0.938$ bits per node
to encode.
