The likelihood-ratio based score level fusion (LR fusion) scheme is known as one of the most promising multibiometric fusion schemes. This scheme verifies a user by computing a log-likelihood ratio (LLR) for each modality, and comparing the total LLR to a threshold. It can happen in practice that genuine LLRs tend to be less than 0 for some modalities (e.g., the user is a “goat”, who is inherently difficult to recognize, for some modalities; the user suffers from temporary physical conditions such as injuries and illness). The LR fusion scheme can handle such cases by allowing the user to select a subset of modalities at the authentication phase and setting LLRs corresponding to missing query samples to 0. A recent study, however, proposed a modality selection attack, in which an impostor inputs only query samples whose LLRs are greater than 0 (i.e., takes an optimal strategy), and proved that this attack degrades the overall accuracy even if the genuine user also takes this optimal strategy. In this paper, we investigate the impact of the modality selection attack in more details. Specifically, we investigate whether the overall accuracy is improved by eliminating “goat” templates, whose LLRs tend to be less than 0 for genuine users, from the database (i.e., restricting modality selection). As an overall performance measure, we use the KL (Kullback-Leibler) divergence between a genuine score distribution and an impostor's one. We first prove the modality restriction hardly increases the KL divergence when a user can select a subset of modalities (i.e., selective LR fusion). We second prove that the modality restriction increases the KL divergence when a user needs to input all biometric samples (i.e., non-selective LR fusion). We conduct experiments using three real datasets (NIST BSSR1 Set1, Biosecure DS2, and CASIA-Iris-Thousand), and discuss directions of multibiometric fusion systems.