  Computing phonons from first-principles is typically considered a solved
problem, yet inadequacies in existing techniques continue to yield deficient
results in systems with sensitive phonons. Here we circumvent this issue using
the lone irreducible derivative (LID) and bundled irreducible derivative (BID)
approaches to computing phonons via finite displacements, where the former
optimizes precision via energy derivatives and the latter provides the most
efficient algorithm using force derivatives. A condition number optimized (CNO)
basis for BID is derived which guarantees the minimum amplification of error.
Additionally, a hybrid LID-BID approach is formulated, where select irreducible
derivatives computed using LID replace BID results. We illustrate our approach
on two prototypical systems with sensitive phonons: the shape memory alloy AuZn
and metallic lithium. Comparing our resulting phonons in the aforementioned
crystals to calculations in the literature reveals nontrivial inaccuracies. Our
approaches can be fully automated, making them well suited for both niche
systems of interest and high throughput approaches.
