  Two types of domain walls exist in magnetically soft cylindrical nanowires:
the transverse-vortex wall (TVW) and the Bloch-point wall (BPW). The latter is
expected to prevent the usual Walker breakdown, and thus enable high domain
wall speed. We showed recently [M. Sch\"obitz \etal, Phys. Rev. Lett. 123,
217201 (2019)] that the previously overlooked OErsted field associated with an
electric current is a key in experiments to stabilize the BPW and reach speed
above 600 m/s with spin-transfer. Here, we investigate in detail this situation
with micromagnetic simulations and modeling. The switching of the azimuthal
circulation of the BPW to match that of the OErsted field occurs above a
threshold current scaling with $1/R^3$ ($R$ is the wire radius), through
mechanisms that may involve the nucleation and/or annihilation of Bloch points.
The domain wall dynamics then remains of a below-Walker type, with speed
largely determined by spin-transfer torque alone.
