  In this work, we study the minimal normal measurement models of quantum
instruments. We show that usually the apparatus' Hilbert space in such a model
is unitarily isomorphic to the minimal Stinespring dilation space of the
instrument.However, if the Hilbert space of the system is infinite dimensional
and the multiplicities of the outcomes of the associated observable (POVM) are
all infinite then this may not be the case. In these pathological cases, the
minimal apparatus' Hilbert space is shown to be unitarily isomorphic to the
instrument's minimal dilation space augmented by one extra dimension. We also
point out errors in earlier papers of one of the authors (J-P.P.).
