The double absorbing boundary (DAB) is a novel extension to the family of high-order absorbing boundary condition operators. It uses auxiliary variables in a boundary layer to set up cancellation waves that suppress wavefield energy at the computational-domain boundary. In contrast to the perfectly matched layer (PML), the DAB makes no assumptions about the incoming wavefield and can be implemented with a boundary layer as thin as three computational grid-point cells. Our implementation incorporates the DAB into the boundary cell layer of high-order finite-difference (FD) techniques, thus avoiding the need to specify a padding region within the computational domain. We tested the DAB by propagating acoustic waves through homogeneous and heterogeneous 3D earth models. Measurements of the spectral response of energy reflected from the DAB indicate that it reflects approximately 10-15 dB less energy for heterogeneous models than a convolutional PML of the same computational memory complexity. The same measurements also indicate that a DAB boundary layer implemented with second-order FD operators couples well with higher-order FD operators in the computational domain. Long-term stability tests find that the DAB and CPML methods are stable for the acoustic-wave equation. The DAB has promise as a robust and memory-efficient absorbing boundary for 3D seismic imaging and inversion applications as well as other wave-equation applications in applied physics.