  The capacity of the quantum dense key distribution (QDKD) [Phys. Rev. A69,
032310 (2004)] is doubled by introducing the dense coding. The security of the
improved QDKD against eavesdropping is pointed out to be easily proven. In both
the original QDKD and the present improved QDKD, a strategy to double the
efficiency of generating the secret key with given length is proposed. In
addition, we point out a leak of security of the original QDKD and fix it.
