Magnetized Liner Inertial Fusion (MagLIF) implosions on the Z accelerator have almost exclusively been driven by 16–20 mega-ampere peak current, ~100 ns rise time pulses. The ~100 ns rise time is selected to be as short as achievable on the Z accelerator partially to maximize liner implosion velocity and to minimize the time during which deleterious implosion instabilities can develop. Modifying the shape of the current pulse could result in benefits to MagLIF including more efficient compression of the liner and fusion fuel, reduced current losses in the pulsed power transmission line (and therefore higher total current delivery to the imploding liner), and more efficient magnetic flux compression in the premagnetized, laser-preheated fusion fuel. We present analysis of three-dimensional magnetohydrodynamic simulations of liner implosions using a 100 ns rise time current pulse and simulations using a current pulse designed to quasi-isentropically compress the liner. Quasi-isentropic compression of the liner prevents formation of shocks in the liner material and the associated longer rise time pulse shape could enable the previously listed beneficial effects. Our analysis focuses on quantifying and comparing the instability development in these simulations. We discuss implications for the potential overall benefits of departing from ~100 ns rise time pulses and employing novel pulse shapes, such as a quasi-isentropic compression pulse, in MagLIF.