An internal model control scheme is proposed to compensate both a long dead-time of a system and a harmonic disturbance. The controller is based on an inversion of the firstorder model used to approximate the system dynamics together with an input delay. Two other components of the controller consist of a filter and an additional delay by which the harmonic modes are targeted via adjusting the control loop gain and phase shift. The design of the filter-delay pair is fully analytical and the implementation of the scheme is straightforward. The main attention is paid to the complete compensation of a single harmonic disturbance. Besides, an extension of the scheme is proposed to target a double harmonic disturbance. Increased attention is paid to the robustness aspects of the schemes. Outstanding performance in terms of harmonic disturbance compensation of the proposed schemes is demonstrated on a series of laboratory experiments.