We suggest a criterion to minimize the amount of fine-tuning in a composite
Higgs model. The paradigm of this type of model is the top-condensate model of
Bardeen, Hill and Lindner (BHL). Although "minimally fine-tuned", this model
failed to account correctly for the masses of the top quark and the 125~GeV
Higgs boson. We propose a generalization of the BHL model that employs
finely-tuned extended technicolor (ETC) plus technicolor (TC) interactions. The
additional freedom of this model may accommodate both m_t(173) and M_H(125).
This paper studies the large-N_{TC} and N_C limit of this model in which
technicolor is weak and does not contribute to electroweak symmetry breaking.
Refinements including walking-TC dynamics and a renormalization group analysis
of m_t and M_H will appear in a subsequent paper. A likely generic signal of
this model is enhanced production of dibosons (W^+W^- and W^\pm Z^0) and
tribosons (W^+W^- Z^0) via rho_T^{0,\pm} and omega_T decay.Comment: 21 pages. Version to be published in Physical Review D (modulo a few
PRD style diktats); paragraph on S-parameter and its status in walking
technicolor models added to Sec. 4 at referee's request; typos fixed in
Appendix equations; reference adde