Temporal envelope-based signal processing strategies are widely used in cochlear-implant (CI) systems. It is well recognized that the inability to convey temporal fine structure (TFS) in the stimuli limits CI users' performance, but it is still unclear how to effectively deliver the TFS. A strategy known as the temporal limits encoder (TLE), which employs an approach to derive the amplitude modulator to generate the stimuli coded in an interleaved-sampling strategy, has recently been proposed. The TLE modulator contains information related to the original temporal envelope and a slow-varying TFS from the band signal. In this paper, theoretical analyses are presented to demonstrate the superiority of TLE compared with two existing strategies, the clinically available continuous-interleaved-sampling (CIS) strategy and the experimental harmonic-single-sideband-encoder strategy. Perceptual experiments with vocoder simulations in normal-hearing listeners are conducted to compare the performance of TLE and CIS on two tasks (i.e., Mandarin speech reception in babble noise and tone recognition in quiet). The performance of the TLE modulator is mostly better than (for most tone-band vocoders) or comparable to (for noise-band vocoders) the CIS modulator on both tasks. This work implies that there is some potential for improving the representation of TFS with CIs by using a TLE strategy.