  We consider a class of Hubbard-Stratonovich transformations suitable for
treating Hubbard interactions in the context of quantum Monte Carlo
simulations. A tunable parameter $p$ allows us to continuously vary from a
discrete Ising auxiliary field ($p=\infty$) to a compact auxiliary field that
couples to electrons sinusoidally ($p=0$). In tests on the single-band Hubbard
model, we find that the severity of the sign problem decreases systematically
with increasing $p$. Selecting $p$ finite, however, enables continuous sampling
methods like the Langevin or Hamiltonian Monte Carlo methods. We explore the
tradeoffs between various simulation methods through numerical benchmarks.
