  We present updated results for the non-perturbative $\beta$-function of SU(3)
gauge theories with $N_f = 12$ or 10 massless flavors in the fundamental rep or
$N_f = 2$ in the sextet rep, measured with staggered fermions. New data at
finer lattice spacing and our previously introduced method, the infinitesimal
$\beta$-function, strengthen the case that the $N_f = 12$ model has no infrared
fixed point up to $g^2 = 7.2$. We show how underestimated cutoff dependence in
one domain wall study for $N_f = 10$ has been corrected, which is now
consistent with staggered results showing a monotonically increasing
$\beta$-function. A consistent theme is that too small volumes can lead to
apparent fixed points which vanish towards the continuum limit. We also apply
the infinitesimal $\beta$-function method to the $N_f = 10$ model, finding
consistent behavior with the finite-step $\beta$-function. Ongoing simulations
and analysis for the sextet model confirm our previous results from weak to
strong coupling with a non-zero $\beta$-function throughout, in quantitative
difference to Wilson fermion simulations~\cite{Hasenfratz:2015ssa}.
