The synthesis of compensators for linear distributed-parameter systems on the basis of a finite-dimensional approximation is a classical technique. This so-called early-lumping approach suffers from the occurrence of spillover which means that the closed-loop dynamics is deteriorated by the neglected dynamics. In this contribution, an early-lumping compensator design is presented that overcomes the spillover problem by using certain fictitious outputs which can be reconstructed without spillover and that suppress the contributions of the unmodelled dynamics. When the new outputs are used for the compensator instead of the available measurements, the perturbation of the closed-loop spectrum, caused by spillover, can be reduced to an arbitrary extent. It is shown that the worst-case eigenvalue perturbation decreases exponentially with respect to the compensator order so that the spillover can be reduced systematically. In addition, an a priori estimate for the compensator order, that guarantees a prescribed maximal eigenvalue perturbation, is presented. The proposed design procedure is demonstrated for the control of an Euler-Bernoulli beam with Kelvin-Voigt damping.