Postspeciation gene flow is widespread across the Tree of Life but is ignored as a cause of gene tree discordance under the standard multispecies coalescent. Where interspecific migration has occurred but is not modelled explicitly, effective population sizes, divergence times and topology can be seriously misestimated. Isolation-with-migration and multispecies coalescent-with-introgression models explicitly model migration but include additional parameters that limit their computational viability with even moderately sized molecular data sets. Here we simulate the evolution of sequences which vary in molecular information content under the coalescent while allowing continuous, tree-wide gene flow/migration between contemporaneous branches, the rate of which decreases with time since divergence. Using simulated sequences, we evaluate the performance of DENIM under rapidly to gradually time-decaying migration and benchmark its performance against the standard MSC method StarBeast3. DENIM consistently outperforms StarBeast3, both in phylogenetic accuracy and computational performance per core. Rapidly decaying migration is associated with improved topology and divergence time estimates under both DENIM and StarBeast3. While species tree estimation accuracy is not improved by increasing the number of loci from 30 to 60 under either method, model convergence is slowed considerably. By contrast, increasing sequence length to 10,000 bp has no clear effect on convergence rates, but shows a tendency towards increased accuracy in DENIM. We apply DENIM and StarBeast3 with a 36-locus empirical bat data set and recover species trees identical in topology to those obtained with 12,931 loci. Our work demonstrates that DENIM can deliver accurate phylogenetic estimates in the presence of both deep coalescence and empirically realistic migration patterns using as few as 30 loci with single-core runtimes of 2-3 days.