Two-dimensional (2-D) finite-difference (FD) synthetics, which fill the gap between fast 1-D analytic synthetics and time-consuming full 3-D synthetics in our ability to model seismograms, have been used in many studies. We address several issues involving 2-D FD methods in generating global synthetic seismograms. These include: (1) interfacing point source excitation for earthquakes with 2-D FD methods; (2) out-of-plane spreading corrections and (3) reducing the spherical Earth to the flattened models. The first issue is tackled using two methods, a ‘transparent source box’ approach and a moment tensor excitation approach, where each has its own advantages. Moreover, our ‘source box’ excitation does not have the late-time drift problem that occurred in previous studies. The out-of-plane geometric spreading correction is accounted for by estimating the ray parameter and applying a post-simulation filter to 2-D synthetics. Finally, parameters of the Earth-flattening transformation are discussed and validated. The effectiveness of this method is demonstrated by comparing our synthetics with frequency–wavenumber summation, normal-mode and 3-D spectral-element synthetics.