  We report on transport in the second Landau level in \emph{in-situ}
back-gated two-dimensional electron gases in GaAs/Al$_x$Ga$_{1-x}$As quantum
wells. Minimization of gate leakage is the primary heterostructure design
consideration. Leakage currents resulting in dissipation as small as $\sim$ 10
pW can cause noticeable heating of the electrons at 10 mK, limiting the
formation of novel correlated states. We show that when the heterostructure
design is properly optimized, gate voltages as large as 4V can be applied with
negligible gate leakage, allowing the density to be tuned over a large range
from depletion to over 4 $\times$ 10$^{11}$ cm$^{-2}$. As a result, the
strength of the $\nu = 5/2$ state can be continuously tuned from onset at n
$\sim 1.2 \times 10^{11}$ cm$^{-2}$ to a maximum $\Delta_{5/2} = 625$ mK at n =
$3.35 \times 10^{11}$ cm$^{-2}$. An unusual evolution of the reentrant integer
quantum Hall states as a function of density is also reported. These devices
can be expected to be useful in experiments aimed at proving the existence of
non-Abelian phases useful for topological quantum computation.
