  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. This pulse
decomposition analysis has previously been performed on a small sample of
bright long bursts using binned data from BATSE, which comes in several data
types, and on a sample of short bursts using the BATSE Time-Tagged Event (TTE)
data type. We have developed an interactive pulse-fitting program using the
phenomenological pulse model of Norris, et al. and a maximum-likelihood fitting
routine. We have used this program 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 present statistical information on
the attributes of pulses comprising these bursts, including relations between
pulse characteristics in different energy channels and the evolution of pulse
characteristics through the course of a burst. We carry out simulations to
determine the biases that our procedures may introduce. We find that pulses
tend to have shorter rise times than decay times, and tend to be narrower and
peak earlier at higher energies. We also find that pulse brightness, pulse
width, and pulse hardness ratios do not evolve monotonically within bursts, but
that the ratios of pulse rise times to decay times tend to decrease with time
within bursts.
