Gamma-ray limits on dark matter annihilation depend on the astrophysical $J$ factor and its uncertainty. Improved determinations of the dark matter distribution can therefore change the interpretation of existing searches even when the gamma-ray data remain unchanged. This contribution summarizes a framework for updating published limits without access to the full experimental likelihood. Within a quadratic approximation, we derive analytical penalty factors describing the effect of Gaussian and log-normal $J$-factor priors. The updated limit follows from the ratio of the old and new central values and penalty factors. The construction also permits the approximate combination of independent targets through one-dimensional root finding. We summarize tests with Poisson ON/OFF simulations, published sensitivity projections, and MAGIC combined limits.