We present a joint analysis of the overlapping Balloon-borne Large Aperture Submillimetre Telescope (BLAST) 250, 350, 500um, and LABOCA 870um observations [from the LABOCA ECDFS Submm Survey (LESS) survey] of the Extended Chandra Deep Field-South. Out to z~3, the BLAST filters sample near the peak wavelength of thermal far-infrared (FIR) emission from galaxies (rest-frame wavelengths ~60-200um), primarily produced by dust heated through absorption in star-forming clouds. However, identifying counterparts to individual BLAST peaks is very challenging, given the large beams [full-width at half-maximum (FWHM) 36-60 arcsec]. In contrast, the ground-based 870um observations have a significantly smaller 19 arcsec FWHM beam, and are sensitive to higher redshifts (z~1-5, and potentially beyond) due to the more favourable negative K-correction. We use the LESS data, as well as deep Spitzer and VLA imaging, to identify 118 individual sources that produce significant emission in the BLAST bands.