Ultra-fast, continuously tunable true-time delays are key components in many microwave and optical communications subsystems. In this paper, we introduce and demonstrate a new implementation method of a continuously tunable true-time delay featuring a settling time in the order of tens of picoseconds. Our solution relies on the splitting and combining of complementary phased shifted spectra (CPSS). It works for large bandwidth signals, has a low complexity, offers moderate losses, and can be fully integrated.