  A `Werner gap' is the range of relevant parameters characterising a quantum
state for which it is both entangled and admits local hidden variable model.
Werner showed that the gap becomes maximal for entanglement mixed with white
noise if subsystems have infinitely many levels. Here we study pure entangled
states mixed with simple coloured noise modelled as a single pure product
state. We provide an explicit local hidden variable model for quantum
correlations of some states of this family and give hints that likely there is
a model for all quantum predictions. This demonstrates essentially maximal
Werner gap already for two qubits. Additionally to fundamental interest the
study has implications for quantum computation and communication.
