  We provide a class of bound entangled states that have positive distillable
secure key rate. The smallest state of this kind is 4 \bigotimes 4. Our class
is a generalization of the class presented in [1] (IEEE Trans. Inf. Theory 54,
2621 (2008); arXiv:quant-ph/0506203). It is much wider, containing, in
particular, states from the boundary of PPT entangled states (all of the states
in the class in [1] were of this kind) but also states inside the set of PPT
entangled states, even, approaching the separable states. This generalization
comes with a price: for the wider class a positive key rate requires, in
general, apart from the one-way Devetak-Winter protocol (used in [1]) also the
recurrence preprocessing and thus effectively is a two-way protocol. We also
analyze the amount of noise that can be admixtured to the states of our class
without losing key distillability property which may be crucial for
experimental realization. The wider class contains key-distillable states with
higher entropy (up to 3.524, as opposed to 2.564 for the class in [1]).
