  We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity
with $R^2$-interaction on spherical topologies, employing Regge's formulation.
We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by
using a finite-size scaling Ansatz in the expectation value of $R^2$, as has
been done in a previous study by Bock and Vink ( hep-lat/9406018 ). By
considerably extending the range and statistics of their study we find that
this Ansatz is plagued by large systematic errors. The $R^2$ specific string
susceptibility exponent $\GS'$ is found to agree with theoretical predictions,
but its determination also is subject to large systematic errors and the
presence of finite-size scaling corrections. To circumvent this obstacle we
suggest a new scaling Ansatz which in principle should be able to predict both,
$\GS$ and $\GS'$. First results indicate that this requires large system sizes
to reduce the uncertainties in the finite-size scaling Ans\"atze. Nevertheless,
our investigation shows that within the achievable accuracy the numerical
estimates are still compatible with analytic predictions, contrary to the
recent claim by Bock and Vink.
