Angle-domain common-image gathers provide much useful data about the subsurface, such as seismic velocities and amplitude-versus-angle (AVA) information, and they can be manipulated to provide high-quality stacked images. However, the computation of angle gathers for reverse time migration (RTM), the most physically accurate migration algorithm, has proven to be costly in terms of computer time and memory usage. We have developed an algorithm for computing RTM angle gathers in a relatively efficient manner. Our method is based on the construction of the directions of propagation of the source and receiver wavefields, given by the direction of energy flux, known as the Poynting vector. The computation is carried out in the space-time domain, avoiding the need to transform the wavefield to, for example, frequency-wavenumber space, as is needed for methods based on wavefront projection. Given accurate Poynting vectors for source and receiver wavefields, one may compute the local reflection angle and azimuth, as well as the reflector dip and azimuth. An important advantage of our method is that it is based on local direction information at the reflection point, and thus it avoids the loss of resolution and smearing that can occur with some other techniques. A simple implementation of the Poynting-vector method can lead to noisy gathers, with leakage between angle bins, caused by unstable division of the local wavefields. We have developed an efficient technique to mitigate this noise and evaluated examples illustrating the aforementioned smearing issues of the subsurface-offset-based gathers and the improvements in the Poynting-vector gathers arising from our algorithm enhancement. Finally, the use of angle gathers for AVA analysis requires that (relative) amplitudes as a function of angle be correct. To this end, we derive weight functions for computing gathers with the correct AVA behavior. We determine the correctness of these weights by testing them with synthetic data.