A simple mathematical model of gamma-ray burst(GRB) pulses in time, suggested by Norris et al., is extended across energy. For a class of isolated pulses, two fit parameters appear to be effectively independent of energy. Specifically, statistical fits indicate that pulse amplitude A and pulse width τ are energy dependent, while pulse start time and pulse shape are effectively energy independent. These results bolster the pulse start and pulse scale conjectures of Nemiroff and add a new pulse shape conjecture which states that a class of pulses all have the same shape. The simple resulting pulse counts model is P(t, E) =A(E) exp[ −t/τ(E) −τ(E)/t], where t is the time since the start of the pulse. This pulse model is found to be an acceptable statistical fit to many of the fluent separable Burst and Transient Source Experiment (BATSE) pulses listed by Norris et al. Even without theoretical interpretation, this cross-energy extension may be immediately useful for fitting prompt emission from GRB pulses across energy channels with a minimal number of free parameters.