Strong yet ductile alloys have long been desired for industrial applications to enhance structural reliability. This work produced two (CoCrNi)93.5Al3Ti3C0.5 medium-entropy alloys with exceptional strength-ductility combinations, via short/medium (3 min/30 min)-time annealing after hot-rolling. Three types of intergranular precipitates including MC, M23C6 carbides, and L12 phase were detected in both the samples. Noticeably, the high density of intragranular L12 precipitates were only founded in the medium-time annealed sample but not in another one. Upon inspection of deformed substructure, it was revealed that the plane slip is the dominant deformation mechanism of both the alloys. This is related to the lower stacking fault energy, higher lattice friction induced by C solute, and slip plane softening caused by intragranular dense L12 precipitates. Additionally, we noted that the stacking fault and twinning act as the mediated mechanisms in deformation of the short-time annealed alloy, while only the former in the medium-time annealed one. It is attributed to the higher energy stacking faults and the increased critical twinning stress caused by intragranular dense L12 precipitates that inhibited the twinning tendency. Our present findings provide not only a guidance for optimizing the mechanical properties of high/medium-entropy alloys, but also a fundamental understanding of deformation mechanisms.