In a series of high performance diverted discharges on DIII-D, we demonstrate that strong negative triangularity (NT) shaping robustly suppresses all edge-localized mode (ELM) activity over a wide range of plasma conditions: ⟨n⟩=0.1-1.5×10^{20} m^{-3}, P_{aux}=0-15 MW, and |B_{t}|=1-2.2 T, corresponding to P_{loss}/P_{LH08}∼8. The full dataset is consistent with the theoretical prediction that magnetic shear in the NT edge inhibits access to ELMing H-mode regimes; all experimental pressure profiles are found to be at or below the infinite-n ballooning stability limit. Our present dataset also features edge pressure gradients in strong NT that are closer to an H-mode than a typical L-mode plasma, supporting the consideration of NT for reactor design.