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Spin-orbit torques with an out-of-plane spin-polarization component are forbidden for spin-current-generating materials with high crystal symmetry, but are permitted for materials with sufficiently low symmetry such as WTe₂ and MoTe₂. However, it remains unclear if symmetry-breaking in the bulk of the spin-current generator is crucial for such torques to exist or if symmetry breaking at the spin-source/magnet interface is sufficient. In addition, it is unclear whether the efficiencies of these torques depend on the spin-orbit coupling strength in the same way as expected for conventional Rashba-type spin-orbit torques. We report measurements of spin-orbit torques generated by ZrTe₃ and other low symmetry materials to understand the existence and strength of the out-of-plane anti-damping spin-orbit torques.