 If the biorthogonal decomposition is applied to the non-perfectly correlated state \(\sum_{ij} d_{ij} \ket{a_i} \otimes \ket{p_j} = \sum_i c_i' \ket{a_i'} \otimes \ket{p_i'}\), according to BDMI the result does not select the pointer \(P\) as a definite-valued property, but a different observable \(P'\) with eigenstates \(\ket{p_i'}\). In this case, in which the selected definite-valued properties are different from those expected, the question arises how different they are. In the case of an imperfect measurement, it may be assumed that the \(d_{ij} \ne 0\), with \(i \ne j\), be small; then, the difference might be also small. But in the case of a disturbing measurement, the \(d_{ij} \ne 0\), with \(i \ne j\), need not be small and, as a consequence, the disagreement between the modal interpretation assignment and the experimental result might be unacceptable (see a full discussion in Bacciagaluppi and Hemmo 1996). This fact has been considered as a “silver bullet” for killing the modal interpretations of the BDMI and SDMI types (Harvey Brown, cited in Bacciagaluppi and Hemmo 1996). This is premature: a fuller analysis involving environmental decoherence is able to remove many of these problems—see below.