  We estimate the impact of weak lensing by strongly nonlinear cosmological
structures on the cosmic microwave background. Accurate calculation of large
$\ell$ multipoles requires N-body simulations and ray-tracing schemes with both
high spatial and temporal resolution. To this end we have developed a new code
that combines a gravitational Adaptive Particle-Particle, Particle-Mesh (AP3M)
solver with a weak lensing evaluation routine. The lensing deviations are
evaluated while structure evolves during the simulation so that all evolution
steps--rather than just a few outputs--are used in the lensing computations.
The new code also includes a ray-tracing procedure that avoids periodicity
effects in a universe that is modeled as a 3-D torus in the standard way.
Results from our new simulations are compared with previous ones based on
Particle-Mesh simulations. We also systematically investigate the impact of box
volume, resolution, and ray-tracing directions on the variance of the computed
power spectra. We find that a box size of $512 h^{-1}$ Mpc is sufficient to
provide a robust estimate of the weak lensing angular power spectrum in the
$\ell$-interval (2,000--7,000). For a reaslistic cosmological model the power
$[\ell(\ell+1)C_{\ell}/2\pi]^{1/2}$ takes on values of a few $\mu K$ in this
interval, which suggests that a future detection is feasible and may explain
the excess power at high $\ell$ in the BIMA and CBI observations.
