  The problem of multilevel diversity coding with secure regeneration is
revisited. Under the assumption that the eavesdropper can access the repair
data for all compromised storage nodes, Shao el al. provided a precise
characterization of the minimum-bandwidth-regeneration (MBR) point of the
achievable normalized storage-capacity repair-bandwidth tradeoff region. In
this paper, it is shown that the MBR point of the achievable normalized
storage-capacity repair-bandwidth tradeoff region remains the same even if we
assume that the eavesdropper can access the repair data for some compromised
storage nodes (type 2 compromised nodes) but only the data contents of the
remaining compromised nodes (type 1 compromised nodes), as long as the number
of type 1 compromised nodes is no greater than that of type 2 compromised
nodes.
