The polychromatic incident energy measurements using chopper spectrometers at pulsed sources enables us to measure dynamics with different energy resolutions, i.e., different time-windows with a single-measurement. By increasing the possible time-window for a single-measurement, the efficiency and usefulness of such measurements is enhanced. This is achieved by allowing the crossing of trajectories of different Eis from different source pulses on the time-of-flight diagram (the interveined trajectory). We will present an actual case of the interveined trajectory on AMATERAS, a cold-neutron chopper spectrometer installed at J-PARC, together with our experience. Some of our attempts to formulate the conditions for performing polychromatic Ei measurements employing interveined trajectories are discussed. These which can be applied to existing spectrometers, and considered as design criteria for future chopper spectrometers. Further related plan of AMATERAS to improve measuring efficiency is also mentioned.