  We have recently learned that the Zeldovich approximation can be successfully
used for a far wider range of gravitational instability scenarios than formerly
proposed; we study here how to extend this range. In previous work we studied
the accuracy of several analytic approximations to gravitational clustering in
the mildly nonlinear regime. We found that the ``truncated Zel'dovich
approximation" (TZA) was better than any other (except in one case the ordinary
Zeldovich approximation) over a wide range from linear to mildly nonlinear
($\sigma \sim 3$) regimes. TZA sets Fourier amplitudes equal to zero for {\it
all} wavenumbers greater than $k_{n\ell}$, where $k_{n\ell}$ marks the
transition to the nonlinear regime. Here, we study crosscorrelation of
generalized TZA with a group of $n$--body simulations for three shapes of
window function: sharp $k$--truncation (as in CMS), tophat in coordinate space,
or a Gaussian. We also study the crosscorrelation as a function of initial
scale within each window type. We find $k$--truncation, which was so much
better than other things tried in CMS, is the {it worst} of these three window
shapes. We find that a Gaussian window $e^{-k^2/2k_G^2}$ applied to the intial
Fourier amplitudes is the best choice. It produces a greatly improved
crosscorrelation all cases we studied. The optimum choice of $k_G$ for the
Gaussian window is (spectrum-- dependent) 1--1.5 times $k_{n\ell}$, with
$k_{n\ell}$ defined by (3). Although all three windows produce similar power
spectra and density distribution functions after application of the Zeldovich
approximation, phase agreement with the $n$--body simulation is better for the
Gaussian window. We ascribe Gaussian window success to its superior treatment
of phase evolution.
