Detailed neutron scattering measurements of YBa_2Cu_3O_6.95 found two magnetic resonance branches of approximately circular symmetry in the a-b plane below T_c. One branch disperses downward from the in-plane wave-vector q_ab=pi/a, pi/a) and ~41 meV toward the spin gap of 33+-1meV. The other, of lower intensity, disperses upward at least to 55 meV. They converge near 41 meV to form the well-known resonance peak. The most striking result is that the q-integrated intensity does not have a maximum at the peak energy, being roughly flat in each of the two branches. The data do not contain any signatures of dynamical magnetic stripes.