  We present a new class of composite Higgs models where an adjustable
tree-level Higgs quartic coupling allows for a significant reduction in the
tuning of the Higgs potential. Our 5D warped space implementation is the first
example of a holographic composite Higgs model with a tree-level quartic. It is
inspired by a 6D model where the quartic originates from the Tr [A_5,A_6]^2
term of the gauge field strength, the same model that led to the original
little Higgs construction of Arkani-Hamed, Cohen, and Georgi. Beyond the
reduction of the tuning and the standard composite Higgs signatures, the model
predicts a doubling of the KK states with relatively small splittings as well
as a Higgs sector with two doublets in the decoupling limit.
