The generalized nucleation theorem as derived by Bowles [J. Chem. Phys. 115, 1853 (2001)] had been verified for nonuniformities generated by a cavity and a cluster within the one-dimensional hard rod fluid. We further verify the nucleation theorem for nonuniformities created by a cavity and by a cluster containing m particles within the internally constrained hard rod fluid. The given results provide additional evidence of the validity of the generalized nucleation theorem even down to the molecular level.