  We compare the convergence of several flat-histogram methods applied to the
2D Ising model, including the recently introduced stochastic approximation with
a dynamic update factor (SAD) method. We compare this method with the
Wang-Landau (WL) method, the $1/t$ variant of the WL method, and standard
stochastic approximation Monte Carlo (SAMC). In addition, we consider a
procedure WL followed by a "production run" with fixed weights that refines the
estimation of the entropy. To our knowledge, this work is the first to test
this approach against other methods. We find that WL followed by a production
run \emph{does} converge to the true density of states, in contrast to pure WL.
Three of the methods converge robustly: SAD, $1/t$-WL, and WL followed by a
production run. Of these, SAD does not require \emph{a priori} knowledge of the
energy range. This work also shows that WL followed by a production run
performs superior to other forms of WL while ensuring both ergodicity and
detailed balance.
