We study current-induced torques in WTe2/permalloy bilayers as a function of WTe2 thickness. We measure the torques using both second-harmonic Hall and spin-torque ferromagnetic resonance techniques for samples with WTe2 thicknesses that span from 16 nm down to a single monolayer. We confirm the existence of an out-of-plane antidamping torque, and we show directly that the sign of this torque component is reversed across a monolayer step in the WTe2. The magnitude of the out-of-plane antidamping torque depends only weakly on WTe2 thickness, such that even a single-monolayer WTe2 device provides a strong torque that is comparable to much thicker samples. In contrast, the out-of-plane fieldlike torque has a significant dependence on the WTe2 thickness. We demonstrate that this fieldlike component originates predominantly from the Oersted field, thereby correcting a previous inference drawn by our group based on a more limited set of samples. © 2017 American Physical Society.