  We derive a new peak lag vs. peak luminosity relation in gamma-ray burst
(GRB) pulses. We demonstrate conclusively that GRB spectral lags are pulse
rather than burst properties and show how the lag vs. luminosity relation
determined from CCF measurements of burst properties is essentially just a
rough measure of this newly derived relation for individual pulses. We further
show that most GRB pulses have correlated properties: short-lag pulses have
shorter durations, are more luminous, and are harder within a burst than
long-lag pulses. We also uncover a new pulse duration vs. pulse peak luminosity
relation, and indicate that long-lag pulses often precede short-lag pulses.
Although most pulse behaviors are supportive of internal shocks (including
long-lag pulses), we identify some pulse shapes that could result from external
shocks.
