Quasi-movements (QMs), which are  movement attempts minimized to the point of movement extinction, evoke EEG patterns similar to those of real movement. QMs can model attempted movement in healthy subjects and are therefore of interest as an alternative to motor imagery (MI) in rehabilitation brain–computer interfaces (BCIs), in which the attempted movement of the paralyzed limb is used as a control signal. Earlier QM studies were focused on thumb abduction. The study aimed to verify the feasibility of QMs based on more natural actions (pressing and pointing) and compare their EEG correlates with those of MI. In 11 healthy volunteers (6 women, aged 21–32), EEG recording was performed during execution of MI, non-goal-directed QMs (nQMs), goal-directed QMs (gQMs), and real movements. Both QM types caused more pronounced contralateral desynchronization of the 8–13 Hz mu rhythm than MI (0.63 dB, effect of movement type, p = 0.042), while nQMs and gQMs did not differ. There were no differences in ipsilateral desynchronization between the conditions (p = 0.216). Pairwise comparisons were significant in the upper-frequency mu rhythm sub-range (nQM–MI: 0.82 dB, p = 0.003; gQM–MI: 0.70 dB, p = 0.022). There was no effect of movement type in the parietal area of interest (p = 0.15). The contribution of residual movement was non-significant. The data obtained show that QMs based on natural actions are feasible and produce stronger sensorimotor activation than MI, which justifies further research focused on QMs in the context of rehabilitation BCIs.