  Two tests for cosmological time dilation in $\gamma$-ray bursts -- the peak
alignment and auto-correlation statistics -- involve averaging information near
the times of peak intensity. Both tests require width corrections, assuming
cosmological origin for bursts, since narrower temporal structure from higher
energy would be redshifted into the band of observation, and since intervals
between pulse structures are included in the averaging procedures. We analyze
long ($>$ 2 s) BATSE bursts and estimate total width corrections for trial
time-dilation factors (TDF = [1+$z_{\rm dim}$]/[1+$z_{\rm brt}$]) by
time-dilating and redshifting bright bursts. Both tests reveal significant
trends of increasing TDF with decreasing peak flux, but neither provides
sufficient discriminatory power to distinguish between actual TDFs in the range
2--3.
