The basic problem of secure bidirectional relaying involves two users who want to exchange messages via an intermediate "honest-but-curious" relay node. There is no direct link between the users, all communication must take place via the relay node. The links between the user nodes and the relay are wireless links with Gaussian noise. It is required that the users' messages be kept secure from the relay. In prior work, we proposed coding schemes based on nested lattices for this problem, assuming that the channel gains from the two user nodes to the relay are identical. We also analyzed the power-rate tradeoff for secure and reliable message exchange using our coding schemes. In this paper, we extend our prior work to the case when the channel gains are not necessarily identical, and are known to the relay node but perhaps not to the users. We show that using our scheme, perfect secrecy can be obtained only for certain values of the channel gains, and analyze the power-rate tradeoff in these cases. We also make similar observations for our strongly-secure scheme.