This paper shows that the poor man's invertibility condition in Fernández-Villaverde et al. (2007) is, in general, sufficient but not necessary for fundamentalness; that is, a violation of this condition does not necessarily imply the impossibility of recovering the structural shocks of a DSGE via a VAR. The permanent income model in Fernández-Villaverde et al. (2007) is used to illustrate this fact. A necessary and sufficient condition for fundamentalness is formulated and its relations with the poor man's invertibility condition are discussed.