Circuits and methods are described for producing a DLL clock signal with adjustable phase shift using a processed control signal. In one embodiment of the invention, a DLL circuit is provided that includes a main and smaller variable delay circuits, a phase detector and an up down counter that provides a main control signal to adjust the delay by the main variable delay circuit. When the DLL circuit is locked, an arithmetic logic unit (ALU) produces a processed control signal based on the main control signal, an ALU control signal and an offset control signal, and the processed control signal is provided to the smaller variable delay circuit. By adjusting the ALU control and offset control signals, the phase shift introduced on the DLL control signal by the smaller variable delay circuit can be adjusted. In another embodiment of the invention, a second up down counter is used in place of an ALU for providing a dynamically adjustable phase shift in accordance with the principles of the present invention.