Numerical estimation of fermionic observables often requires introduction of auxiliary bosonic fieldsthat have no direct physical relevance through a Hubbard-Stratonovich transformation. The varianceof some fermionic observables (for example, appropriately constructed local four-fermion operatorsin 2d Gross-Neveu model) when they are estimated using such auxiliary fields may not correspondto any physical observable and in particular may diverge. In such cases it is not clear how onecan reliably estimate the corresponding observable. An important example may be found in thecontext of exceptional configurations in quenched QCD. We demonstrate simpler examples in toymodels by constructing particular four-fermion operators. We propose two methods to overcome thisissue. The first method is a discrete Hubbard-Stratonovich transformation that does not suffer fromsuch divergences for these classes of observables. While this method works in principle, it is notpractically feasible. The second method we propose is a reweighting method.