We investigate resolution capabilities of adaptive thresholding methods in the context of iterative microwave imaging algorithms. Our test cases involve two closely located cylindrical targets of high dielectric contrast with respect to the background in a microwave tomography setup simulated in CST. We apply a distorted Born iterative method (DBIM), and compare a two-step iterative shrinkage thresholding (TwIST) implementation with a conventional conjugate gradient least squares (CGLS) method as linear solvers at each DBIM iteration. Our results demonstrate that applying the TwIST approach can resolvethetwoclosely-locatedtargetsmuchmoreaccuratelythan the CGLS under identical settings in the DBIM algorithm