[en] A typical pulse from the 807 calorimeter is shown. This was generated by 4 GeV electrons but the pulses from hadrons and at different energies are not significantly different. The width and shape of this pulse comes from the convolution of a number of sources: (a) The time spread of energy deposition by a shower including time of flight of slow protons and neutrons, (b) scintillator phosphor rise and decay times, (c) shifter rise and decay times, (d) phototube response, (e) time delays in the light collection from different parts of the calorimeter and time dispersion in transmission. The objective of the first phase of this study was to isolate these spearate contributions, estimate how they could be speeded up and find what costs are involved. In the second phase we constructed an extremely crude calorimeter whose pulses should have the same characteristic as in a real device. With this we have observed signals whose mean width was 7 nsec and whose width at 10% of maximum height was 15 nsec. Clipping could reduce these widths to 6 and 12 nsec respectively. We conclude that gate times of less than 20 nsec would be appropriate for such a calorimeter