The ground state of a many-electron system can be projected from a trial state using an integral of one-electron projectors over a set of Hubbard-Stratonovich auxiliary fields. We have explored several alternative formulations of this method and find that the convergence of the ground-state energy with the number of field variables can be dramatically improved by choosing the appropriate one. This is illustrated using the two-dimensional Hubbard model as an example. These results are also used to examine the error associated with neglecting the so-called ‘‘sign problem’’ common to quantum Monte Carlo many-fermion calculations.