We update a fast method for calculating the global mean radiative efficiency (RE) for weak absorbers (known as the Pinnock Curve). It is then employed to evaluate improved REs, for 30 halocarbons focusing particularly on the low-wavenumber (<500 cm^-1) contributions where laboratory measurements of absorption cross-sections are scarce. The Pinnock Curve is updated using spectral line parameters from the HITRAN2020 database and the MT_CKD_4.3 water vapor continuum formulation. Halocarbon REs are evaluated by coupling this update with infrared absorption cross section spectra evaluated by means of a quantum chemical protocol featuring a non-empirical inclusion of anharmonic effects in both transition frequencies and intensities and accounting for conformer distributions. Recent revisions to the MT_CKD water vapor continuum coefficients decrease atmospheric opacity, producing a small increase in RE, which is counteracted by updates to line-by-line spectroscopic parameters in HITRAN2020. These compensatory effects result in a small increase in halocarbon REs, with an average rise of ~0.3 %. Analysis of the low-wavenumber region shows that for the targeted compounds it contributes no more than 5 mW m^-2ppb^-1. On average, it amounts to 0.9 % of the total RE, but reaches about 3 % for HFC-152a and HFC-161. Despite this modest magnitude, accurate treatment of this spectral range is essential, as its impact is molecule-dependent and even small contributions can influence climate metrics. For seven of the 30 gases considered here, the low frequency contribution to RE is more than 10 times greater than that calculated in earlier work.