We present a study of the $D$ and $B$ leptonic decay constants on the MILC $N_f=2+1$ asqtad gauge ensembles using asqtad-improved staggered light quarks and clover heavy quarks in the Fermilab interpretation. Our previous analysis \cite{Bazavov:2011aa} computed the decay constants at lattice spacings $a ≈ 0.14, 0.11$ and $0.083$ fm. We have extended the simulations to finer $a ≈ 0.058$ and $0.043$ fm lattice spacings, and have also increased statistics; this allows us to address many important sources of uncertainty. Technical advances include a two-step two-point fit procedure, better tuning of the heavy quark masses and a better determination of the axial-vector current matching. The present analysis remains blinded, so here we focus on the improvements and their predicted impact on the error budget compared to the prior analysis. ; Comment: LATTICE 2013; added missing .bbl file