This paper explores the sensitivity of 2D wave effects to crucial problem parameters, such as the frequency content of the base motion, its details, and soil nonlinearity. A numerical study is conducted, utilizing a shallow soft valley as a test case. It is shown that wave focusing effects near valley edges and surface waves generated at valley corners are responsible for substantial aggravation (AG) of the seismic motion. With high-frequency seismic excitation, 1D soil amplification is prevailing at the central part of the valley, while 2D phenomena are localized near the edges. For low-frequency seismic excitation, wave focusing effects are overshadowed by laterally propagating surface waves, leading to a shift in the location of maximum AG toward the valley center. If the response is elastic, the details of the seismic excitation do not seem to play any role on the focusing effects at valley edges, but make a substantial difference at the valley center, where surface waves are dominant. The increase of damping mainly affects the propagation of surface waves, reducing AG at the valley center, but does not appear to have any appreciable effect at the valley edges. Soil nonlinearity may modify the 2D valley response significantly. For idealized single-pulse seismic excitations, AG at the valley center is reduced with increasing nonlinearity. Quite remarkably, for real multicycle seismic excitations AG at the valley edges may increase with soil nonlinearity. In contrast to the vertical component of an incident seismic motion, which is largely the result of P waves and is usually of too high frequency to pose a serious threat to structures, the valley-generated parasitic vertical component could be detrimental to structures: being a direct result of 2D wave reflections/refractions, it is well correlated and with essentially the same dominant periods as the horizontal component.