  We discuss stiffening of dense matter in two color QCD (QC$_2$D) where
hadrons are mesons and diquark baryons. We study two models which describe a
transition of matter from the Bose-Einstein-Condensation regime at low density
to the Bardeen-Cooper-Schrieffer regime at high density. The first model is
based on coherent states of diquarks, and the second is the Nambu-Jona-Lasinio
model with diquark pairing terms. We particularly focus on how quark states are
occupied as baryon density increases. We find that, due to the occupied quark
levels, the ideal gas picture of diquarks breaks down at density significantly
less than the density where baryon cores overlap. The saturation of quark
states at low momenta stiffens equations of state. We also study the effects of
interactions which depend on the quark occupation probability. We argue that
equations of state become very stiff when the bulk part of the quark Fermi sea
has the effective repulsion but the Fermi surface enjoys the attractive
correlations. This disparity for different momentum domains is possible due to
the strong channel dependence in gluon exchanges with momentum transfer of
$0.2-1$ GeV. These concepts can be transferred from QC$_2$D to QCD in any
numbers of colors.
