Vertical shears of horizontal winds play an important role in the dynamics of the middle and upper atmosphere. Prior observations have indicated that these shears predominantly occur in the lower thermosphere. MIGHTI observations from the Ionospheric Connection Explorer indicate that strong wind shears are a common feature of the lower thermosphere and vary greatly between orbits. This work focuses on these strong shears, and examines their occurrences, horizontal scales and underlying organization. No preferred wind shear direction is found. The shears that persist for a short horizontal extent are slightly larger in amplitude and more numerous than those that persist across large horizontal scales. The altitude at which the strongest shears occur often shows a downward progression with local time, following the climatological winds. Consistent with prior observations, the strongest shears are often seen just below the wind maximum, which follows the downward phase propagation consistent with upward propagating tides.