We report a systematic experimental investigation of single-particle lifetimes in quasi-one-dimensional structures. The lifetimes were measured in GaAs quantum wires of variable width and carrier density. Experimental data show excellent agreement with theoretical estimates that use a single fitting parameter. The data also suggest that the dominant relaxation mechanism for single-particle excitations in these structures at low temperature is remote impurity scattering. Additionally, we find that the electrostatic confining potential along the width of these structures is parabolic in shape, which agrees with existing theoretical predictions.