Under quite likely conditions, data measurement errors can cause an (upward) bias in unidimensional poverty estimates and thus mislead both conceptual analyses and policy implications. In the case of multidimensional poverty, we find that by proposing a dual cut-off strategy, the Alkire-Foster method will typically attenuate this bias. With data from a 2010 Living Standard Measurement Survey (LSMS) from Peru, we find empirical evidence in support of this virtue of the dual cut-off strategy.