<p>Identification of vulnerable meters is a prerequisite for implementing protection-based defense against false data injection attacks targeting power system state estimation. However, since determining the vulnerability of meters is a complex problem, the existing methods make the following assumptions to arrive at a solution: (i) only a few attack vectors are considered for vulnerability determination and (ii) there is no differentiation between the sparsest attack vectors. Accuracy of the solution is not guaranteed because of these approximations. Considering the importance of obtaining an accurate vulnerability measure, this paper proposes a method to overcome the limitations due to these approximations. First, a method to obtain bounds on the vulnerability index is proposed; the method based on bounds can consider a large number of attack vectors. Second, a computationally efficient method is proposed along with the proposed bounds to combine the results obtained for individual sparsest attack vectors, making it possible to differentiate between the sparsest attack vectors. Case studies on the EEE 118-bus system show that the result can change if the approximations/assumptions made in the existing methods are removed, highlighting the relevance of the proposed method.</p>