Digital signature mechanism with appendix(DSwA) is a type of digital signature in which, after the message, a signature Σ is appended. When DSwA is constructed based on the discrete logarithm problem, Σ is composed of a pair (R,S). When R is a hashcode with bit length γ and S is an element of subgroup of order q with bit length β, it is recommended to adjust γ and β to be similar because the security strength depends on the smaller value between γ and β. However in some circumstances only hash functions with longer output could be available. Then γ becomes unnecessarily longer than β, and hence the longer Σ is appended. For the above case, we propose a generalized method for reducing the size of Σ by truncating R by β without loss of any security strength. Our proposed method can be applied to mechanisms like KCDSA, SDSA, EC-KCDSA, and EC-SDSA in ISO/IEC 14888-3: Digital signatures with appendix — Part 3: Discrete logarithm based mechanisms.