  Two-Bar Charts Packing Problem is to pack $n$ two-bar charts (2-BCs) in a
minimal number of unit-capacity bins. This problem generalizes the strongly
NP-hard Bin Packing Problem. We prove that the problem remains strongly NP-hard
even if each 2-BC has at least one bar higher than 1/2. Next we consider the
case when the first (or second) bar of each 2-BC is higher than 1/2 and show
that the $O(n^2)$-time greedy algorithm with preliminary lexicographic ordering
of 2-BCs constructs a packing of length at most $OPT+1$, where $OPT$ is
optimum. Eventually, this result allowed us to present an $O(n^{2.5})$-time
algorithm that constructs a packing of length at most $4/3\cdot OPT+2/3$ for
the NP-hard case when each 2-BC has at least one bar higher than 1/2.
