The search for a finite CP-violating neutron electric dipole moment (nEDM) is motivated in order to understand the observed large matter-antimatter asymmetry in our universe. It has become a worldwide endeavour which is followed by various research teams setting up experiments for improved measurements. Recently, a novel concept to measure a nEDM has been brought forward [F.M. Piegsa, Phys. Rev. C 88, 045502 (2013)]. It foresees to employ a pulsed neutron beam instead of the established use of storable so-called ultracold neutrons (UCN). The new technique takes advantage of the high peak intensity and the intrinsic time structure of next-generation pulsed spallation sources to directly measure the previously limiting relativistic effect. Such an experiment, e.g. set up at the planned European Spallation Source ESS in Sweden, would be complementary to planned experiments with UCN and could compete with their sensitivities. In this talk, I will describe this alternative approach and first test experiments performed at the spallation neutron source SINQ at the Paul Scherrer Institute in Switzerland. These experiments also include related measurements concerning the search for exotic spin-dependent short range forces [Piegsa & Pignol, Phys. Rev. Lett. 108, 181801 (2012)].