Acoustic radiation torque (ART) plays an important role in the subject of acoustophoresis, which could induce the spinning rotation of particles on their own axes. The partial wave series method (PWSM) and T matrix method (TMM) are employed to investigate the three-dimensional radiation torques of both spherical and nonspherical objects in a single Bessel beam over broader frequencies (from Rayleigh scattering to geometric-optics regimes), with emphasis on the parametric conditions for torque reversal and the corresponding physical mechanisms. For elastic objects, the dipole, quadrupole, and even several higherscattering modes are dominant to induce the axial ARTs beyond the Rayleigh limit with a relatively large offset from the particle centroid to the beam axis in Bessel beams. The reversals appear with parametric conditions (including wave number, cone angle, and offset) for the extrema or null values of the corresponding cylindrical Bessel functions. The reversal of transverse ART from a rigid nonspherical particle is also investigated in an ordinary Bessel beam and the geometrical surface roughness is briefly studied for the effect on the radiation torques. This suggests the possibility of acoustic tweezers controlling the spinning motion of particles within and beyond the Rayleigh limit.