  The time profiles of many gamma-ray bursts consist of distinct pulses, which
offers the possibility of characterizing the temporal structure of these bursts
using a relatively small set of pulse shape parameters. We have used a pulse
decomposition procedure to analyze the Time-to-Spill (TTS) data for all bursts
observed by BATSE up through trigger number 2000, in all energy channels for
which TTS data is available. We obtain amplitude, rise and decay timescales, a
pulse shape parameter, and the fluences of individual pulses in all of the
bursts. We investigate the correlations between brightness measures (amplitude
and fluence) and timescale measures (pulse width and separation) which may
result from cosmological time dilation of bursts, or from intrinsic properties
of burst sources or from selection effects. The effects of selection biases are
evaluated through simulations. The correlations between these parameters among
pulses within individual bursts give a measure of the intrinsic effects while
the correlations among bursts could result both from intrinsic and cosmological
effects. We find that timescales tend to be shorter in bursts with higher peak
fluxes, as expected from cosmological time dilation effects, but also find that
there are non-cosmological effects contributing to this inverse correlation. We
find that timescales tend to be longer in bursts with higher total fluences,
contrary to what is expected from cosmological effects. We also find that peak
fluxes and total fluences of bursts are uncorrelated, indicating that they
cannot both be good distance indicators for bursts.
