  Reducing memory traffic is critical to accelerate Lattice QCD computations on
modern processors, given that such computations are memory-bandwidth bound. A
commonly used strategy is mixed-precision solvers, however, these require
careful treatment to ensure stable convergence. We give an overview of the
strategies employed in QUDA to stabilize mixed-precision variants of Conjugate
Gradient (CG), and its multi-shift brethren. Through the use of customized
numerical storage formats we can significantly improve upon the precision
achievable compared to IEEE numerical formats, increasing both the solver
precision and stability achievable at fixed word size. We give examples using
BiCGStab(l) and multi-shift CG solvers using the HISQ operator.
