There is an important need for seismologists and engineers to determine seismic displacement including its quasi-static components. The existence of commercial low-cost and low-noise instruments has prompted researchers to try to derive displacement-time histories from acceleration records by using different integration techniques. In this article we show that an important reason for the failure of the integration process is the presence, in translational acceleration records, of tilt effects or rotational components of motions. The importance of these effects in seismic records has been considered in analytical studies before. In this work we show, using controlled experimental tests on a six-component shake table, that small tilts generate a distortion of the translational acceleration records that limits their validity, especially for low-frequency components. We show that knowledge of the complete history of tilt is necessary to obtain an accurate displacement after a double-time integration and that the knowledge of the initial and final tilt magnitudes is not sufficient to obtain the true displacements. Hence, it is crucial, as a minimum, to record at the same place and at the same time the complete time history of the three rotational and the three translational components or to have a non-rotation-sensitive instrument to calculate properly the translational ground displacement, including its permanent components.