We present an experimental demonstration of additive point source localization (APSL), a sparse parametric imaging algorithm that reconstructs the 3-D positions and activities of multiple gamma-ray point sources. Using a handheld gamma-ray detector array and up to four 8 mu Ci 137Cs gamma-ray sources, we performed both source-search and source-separation experiments in an indoor laboratory environment. In the majority of the source-search measurements, APSL reconstructed the correct number of sources with position accuracies of 20 cm and activity accuracies (unsigned) of 20%, given measurement times of 2 to 3 min and distances of closest approach (to any source) of 20 cm. In source-separation measurements where the detector could be moved freely about the environment, APSL was able to resolve two sources separated by 75 cm or more given only 60 s of measurement time. In these source-separation measurements, APSL produced larger total activity errors of 40%, but obtained source-separation distances accurate to within 15 cm. We also compare our APSL results against traditional maximum likelihood-expectation maximization (ML-EM) reconstructions and demonstrate improved image accuracy and interpretability using APSL over ML-EM. These results indicate that APSL is capable of accurately reconstructing gamma-ray source positions and activities using measurements from existing detector hardware.