Lifetimes of the first excited 2+ states in the extremely neutron-deficient 162W and 164W nuclei have been measured using the recoil distance Doppler shift technique. Experimental B(E2) data for the isotopic chains of hafnium, tungsten, and osmium, from the midshell region near the β-stability line towards the N = 82 closed shell and the most neutron-deficient nuclides, are compared with predictions of nuclear deformations and 21 + → 0g.s. + reduced transition strengths from different classes of state-of-the-art theoretical model calculations. The results reveal striking differences and deficiencies in the predictive power of current nuclear structure models.