Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equation Tx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution Mathematical expression belongs to the range of the operator (T*T)v, o<v≤1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate if v=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2≤v≤1. © 1994 Plenum Publishing Corporation.