  We construct renormalizable Standard Model extensions, valid up to the Planck
scale, that give a composite Higgs from a new fundamental strong force acting
on fermions and scalars. Yukawa interactions of these particles with Standard
Model fermions realize the partial compositeness scenario. Under certain
assumptions on the dynamics of the scalars, successful models exist because
gauge quantum numbers of Standard Model fermions admit a minimal enough 'square
root'. Furthermore, right-handed SM fermions have an SU(2)$_R$-like structure,
yielding a custodially-protected composite Higgs. Baryon and lepton numbers
arise accidentally. Standard Model fermions acquire mass at tree level, while
the Higgs potential and flavor violations are generated by quantum corrections.
We further discuss accidental symmetries and other dynamical features stemming
from the new strongly interacting scalars. If the same phenomenology can be
obtained from models without our elementary scalars, they would reappear as
composite states.
