  Using the existing simplified model framework, we build several dark matter
models which have suppressed spin-independent scattering cross section. We show
that the scattering cross section can vanish due to interference effects with
models obtained by simple combinations of simplified models. For weakly
interacting massive particle (WIMP) masses $\gtrsim$10 GeV, collider limits are
usually much weaker than the direct detection limits coming from LUX or
XENON100. However, for our model combinations, LHC analyses are more
competitive for some parts of the parameter space. The regions with direct
detection blind spots can be strongly constrained from the complementary use of
several Large Hadron Collider (LHC) searches like mono-jet, jets + missing
transverse energy, heavy vector resonance searches, etc. We evaluate the
strongest limits for combinations of scalar + vector, "squark" + vector, and
scalar + "squark" mediator, and present the LHC 14 TeV projections.
