  For a tripartite pure state of three qubits, it is well known that there are
two inequivalent classes of genuine tripartite entanglement, namely the
GHZ-class and the W-class. Any two states within the same class can be
transformed into each other with stochastic local operations and classical
communication (SLOCC) with a non-zero probability. The optimal conversion
probability, however, is only known for special cases. Here, we derive new
lower and upper bounds for the optimal probability of transformation from a
GHZ-state to other states of the GHZ-class. A key idea in the derivation of the
upper bounds is to consider the action of the LOCC protocol on a different
input state, namely $1/\sqrt{2} [\ket{000} - \ket{111}]$, and demand that the
probability of an outcome remains bounded by 1. We also find an upper bound for
more general cases by using the constraints of the so-called interference term
and 3-tangle. Moreover, we generalize some of our results to the case where
each party holds a higher-dimensional system. In particular, we found that the
GHZ state generalized to three qutrits, i.e., $\ket{\mathrm{GHZ}_3} =
1/\sqrt{3} [ \ket{000} + \ket{111} + \ket{222} ] $, shared among three parties
can be transformed to {\it any} tripartite 3-qubit pure state with probability
1 via LOCC. Some of our results can also be generalized to the case of a
multipartite state shared by more than three parties.
