  The Randall Sundrum (RS) models receive significant constraints from the
neutral Kaon system. The CP violating observable $\epsilon_K$, in Randall
Sundrum scenario, requires the lightest KK gluon to be heavier than $\sim$ 24
TeV. The constraint is even stronger in the Little Randall Sundrum models
(LRS), $\gtrsim$ 32 TeV. The LRS models are motivated for their possible
visibility at the Large Hardon Collider (LHC). We show that the stringent
constraints from K-physics can be relaxed in the LRS models, in the presence of
the Brane Localised Kinetic Terms (BLKT). In particular, for a range of values,
a UV BLKT could significantly modify the lightest KK gluon wave function such
that the limit can reduces to 5 TeV. We also show that such a relaxation of the
constraints can also be achieved by imposing flavour symmetries {\`a la }
Minimal Flavour Protection.
