Using a variant of the laser photoelectron attachment (LPA) method with an extended energy range (EXLPA), we have studied low-energy electron attachment to the molecules CCl₄ (Cl⁻ and Cl⁻₂ formation) and SF₆ (SF⁻₆ and SF⁻₅ formation) in a diffuse gas target (T_G = 300 K) from 0 eV up to 2 eV at energy widths down to 14 meV. In the EXLPA method, pulses of near-zero energy photoelectrons are produced in a guiding magnetic field, accelerated by a weak electric field, brought to the energy of interest prior to their traversal through the target region and subsequently accelerated and deflected onto a detecting plate. Anions due to electron attachment are extracted by a pulsed electric field, during which the photoelectron current is interrupted, and detected by a quadrupole mass spectrometer. The EXLPA anion yields are combined with absolute cross sections, obtained at very high resolution (≈1 meV) with the LPA method over the range 0–0.17 eV, to yield new recommended absolute partial and total attachment cross sections over the range 0–2 eV at the well-defined gas temperature T_G = 300 K. Our cross sections show characteristic deviations from previously reported results. At least in part, these differences can be attributed to the fact that in the earlier electron beam experiments the gas temperature was higher than 300 K. For SF₆, the branching fractions for SF⁻₅ formation at electron energies 0.002–0.43 eV and for different initial rovibrational distributions are compared with those recently predicted from kinetic modelling within the framework of statistical unimolecular rate theory. Satisfactory agreement is observed, but our data provide evidence that an additional path for producing SF⁻₆ and SF⁻₅ ions is available at electron energies above about 0.3 eV.