Previous work has shown that a set of two diffractive optical elements arranged in series can form a diffractive lens with variable optical power that can be tuned by relative rotation of its two sub-elements about their common central axis. However, previous designs of these diffractive optical elements did not take advantage of the full spatial resolution required for the fabrication process because the corresponding sub-elements consisted of both, regions with very high phase gradients (requiring full resolution) and other extended regions with nearly vanishing phase gradients, where the available resolution is "wasted". Here, an advanced design is proposed that exploits the full spatial bandwidth of the production system. This is done by increasing the polar (angular) phase gradient of each sub-element such that it approaches the usually much larger radial phase gradient. A pair of these new sub-elements then composes a diffractive lens that has the same tuning range of its optical power than a standard tunable diffractive lens, but advantageously achieved within a much smaller relative rotation range. This has advantages in systems where high speed tuning of optical power is required, and in systems where the rotation angle is limited.