Random compact gauge transformations can partially restore gauge invariance to a lattice simulation that is guided by a non-compact action that is not itself gauge invariant. Various ways of implementing this procedure have been applied to pure SU(2) gauge theory on a lattice, and Wilson loops have been measured at strong coupling, , and at moderate couplings, and 2. The Wilson loops display a confinement signal not seen in simulations performed earlier with the same action but without the random gauge transformations. In general this confinement signal is stronger when the gauge transformations are more frequent and more random.