Lead-free perovskites are attracting increasing interest as nontoxic materials for advanced optoelectronic applications. Here, we report on a family of silver/bismuth bromide double perovskites with lower dimensionality obtained by incorporating phenethylammonium (PEA) as an organic spacer, leading to the realization of two-dimensional double perovskites in the form of (PEA)(4)AgBiBr8 (n = 1) and the first reported (PEA)(2)CsAgBiBr7 (n = 2). In contrast to the situation prevailing in lead halide perovskites, we find a rather weak influence of electronic and dielectric confinement on the photophysics of the lead-free double perovskites, with both the 3D Cs2AgBiBr6 and the 2D n = 1 and n = 2 materials being dominated by strong excitonic effects. The large measured Stokes shift is explained by the inherent soft character of the double-perovskite lattices, rather than by the often-invoked band to band indirect recombination. We discuss the implications of these results for the use of double perovskites in light-emitting applications.