  We explore the influence of progenitor mass and rotation on the
gravitational-wave (GW) emission from core-collapse supernovae, during the
postbounce, preexplosion, accretion-phase. We present the results from 15
two-dimensional (2D) neutrino radiation-hydrodynamic simulations from initial
stellar collapse to $\sim$300 ms after core bounce. We examine the features of
the GW signals for four zero-age main sequence (ZAMS) progenitor masses ranging
from 12 $M_\odot$ to 60 $M_\odot$ and four core rotation rates from 0 to 3 rad
s$^{-1}$. We find that GW strain immediately around core bounce is fairly
independent of ZAMS mass and---consistent with previous findings---that it is
more heavily dependent on the core angular momentum. At later times, all
nonrotating progenitors exhibit loud GW emission, which we attribute to
vibrational g-modes of the protoneutron star (PNS) excited by convection in the
postshock layer and the standing accretion shock instability (SASI). We find
that increasing rotation rates results in muting of the accretion-phase GW
signal due to centrifugal effects that inhibit convection in the postshock
region, quench the SASI, and slow the rate at which the PNS peak vibrational
frequency increases. Additionally, we verify the efficacy of our approximate
general relativistic (GR) effective potential treatment of gravity by comparing
our core bounce GW strains with the recent 2D GR results of other groups.
