One of the fundamental properties of the Mandelbrot set is that the set of postcritically finite parameters is structured like a tree. We extend this result to the set of quadratic kneading sequences and show that this space contains no irrational decorations. Along the way, we prove a combinatorial analogue to the correspondence principle of dynamic and parameter rays. Our key tool is to work simultaneously with the two equivalent combinatorial concepts of Hubbard trees and kneading sequences.