Long-chain branched polymer melts such as low density polyethylene (LDPE) and branched metallocene polyethylenes show strong time-strain separability in step strain. Constitutive models of the multi-mode Pom-pom form are highly successful in modeling the stress generated by general flow histories for these materials. However, a single Pom-pom mode is not time-strain separable and reconciling this to the step-strain phenomenon has been a challenge. We investigate multi-mode integral Pom-pom models and a differential approximation to compare time-strain separation, with respect to mode density. Here we show that for a wide class of branched distributions, a family of damping functions can be derived with a response that is very close to separable. We evaluate the family for both LDPE and branched high density polyethylene melts and show that a damping function derived from the multi-mode Pom-pom model gives an accurate prediction of the damping behavior in step-strain experiments.