Neutron-deficient osmium isotopes ¹⁶⁶Os and ¹⁶⁸Os have been studied with γ-ray spectroscopy and lifetime measurements. The level scheme of ¹⁶⁶Os has been expanded with several new structures including second the 8+ and 10+ states. These states confirm the change in the structure of the yrast band between the 6+ and 8+ states. Lifetimes of the low-lying excited states have been measured in an RDDS measurement. The results reveal a sudden decrease in the collectivity when moving towards the neutron shell closure. While the 2+ → 0+ transition is still collective in ¹⁶⁸Os, in ¹⁶⁶Os the reduced transition probability is only few Weisskopf units, a value expected only at closed shells. In ¹⁶⁸Os the 4+ → 2+ transition is remarkably less collective than the 2+ → 0+ transition. While nuclear models predict a decrease in collectivity, no modern calculations can explain the measured transition probabilities.