The compression of multi-frequency cosmic microwave background (CMB) power spectrum measurements into a series of foreground-marginalised CMB-only band powers allows for the construction of faster and more easily interpretable 'lite' likelihoods. However, obtaining the compressed data vector is computationally expensive and yields a covariance matrix with sampling noise. In this work, we present an implementation of the CMB-lite framework relying on automatic differentiation. The technique presented reduces the computational cost of the lite likelihood construction to one minimisation and one Hessian evaluation, which run on a personal computer in about a minute. We demonstrate the efficiency and accuracy of this procedure by applying it to the differentiable SPT-3G 2018 TT /TE/EE likelihood from the candl library. We find good agreement between the marginalised posteriors of cosmological parameters yielded by the resulting lite likelihood and the reference multifrequency version for all cosmological models tested; the best-fit values shift by <0.1 σ, where σ is the width of the multi-frequency posterior, and the inferred parameter error bars match to within 10%. We publicly release the SPT-3G 2018 TT /TE/EE lite likelihood and a python notebook showing its construction on the candl website.