Levels in 166Er have been studied with the 164Er(t, p) and 168Er(p, t) reactions using beams of 17 MeV tritons and 18 MeV protons. The reaction products were analysed with a magnetic spectrograph. Iπ = 0+ levels populated in these reactions could be readily identified from the characteristic L = 0 angular distributions, and new 0+ states have been discovered at 1713 and 1935 keV. The previously known 1460 keV 0+ state and the one at 1713 keV are both strongly populated in the (t, p) reaction. Contrary to the findings of a previous study, the (p, t) reaction also has a large amount of L = 0 strength to excited states in 166Er, in particular to the 1713, 1935 and 2196 keV levels. These results agree well with the systematics of two-neutron transfer strengths to excited 0+ states in this mass region.