  An approximation of the Standard Regge Calculus (SRC) was proposed by the
$Z_2$-Regge Model ($Z_2$RM). There the edge lengths of the simplicial complexes
are restricted to only two possible values, both always compatible with the
triangle inequalities. To examine the effect of discrete edge lengths, we
define two models to describe the transition from the $Z_2$RM to the SRC. These
models allow to choose the number of possible link lengths to be $n =
{4,8,16,32,64,...}$ and differ mainly in the scaling of the quadratic link
lengths. The first extension, the $X^1_n$-Model, keeps the edge lengths limited
and still behaves rather similar to the "spin-like" $Z_2$RM. The vanishing
critical cosmological constant is reproduced by the second extension, the
$X^C_n$-Model, which allows for increasing edge lengths. In addition the area
expectation values are consistent with the scaling relation of the SRC.
