Light curves, Rayleigh-Taylor instability, and nucleosynthesis of exploding helium stars are examined to look for relevant models for Type Ib supernovae, especially for SN 1983N and 19831 whose light curves decline as fast as Type Ia supernovae. The calculated light curves show a systematic dependence on the stellar mass, because smaller mass helium stars undergo more extensive mixing and eject smaller mass, thereby forming light curves with steeper tails. The relatively fast decline of the SN Ib light curves can thus be accounted for by the helium star models if the helium star mass is as low as 3-4 M⊙ and if 56Ni is mixed to the surface layers. Moreover, the 3-4 M⊙ helium stars, having relatively small mass iron cores, can produce ∼0.15 M⊙ 56Ni as required from the maximum luminosities. In terms of nucleosynthesis, mixing, and light curves, the helium stars of 3-4 M⊙ (which form from stars with Mms ∼ 12-16 M⊙ in binary systems) are the most relevant progenitors of the Type Ib supernovae 1983N and 19831.