Current-induced spin-transfer torque in spin valve structures with magnetic layers made of different materials can exhibit a nonstandard, i.e., wavy like, angular variation. Following the diffusive spin transport model, the wavy torque was theoretically found in the Co(8 nm)/Cu(10 nm)/Py(8 nm) spin valve, and later was also experimentally confirmed. However, the single domain (macrospin) approximation fails to describe some features of magnetic dynamics observed in experiments, especially the frequency agility with current and its slope for the out-of-plane precessions. Therefore, we have revisited the abovementioned pillar structure and analyzed the conditions for the appearance of the out-of-plane oscillations. In particular, we have studied the possibility of triggering these modes by means of a moderate external magnetic field. We have identified modes supported within the macrospin model and verified the results by full micromagnetic simulations, revealing numerous qualitative discrepancies. For instance, the out-of-plane oscillations have been found in the macrospin model, whereas no such precessions have been observed in micromagnetic simulations even with an external magnetic field.