Many functional materials are difficult to analyze by Scanning Transmission Electron Microscopy (STEM) on account of their beam sensitivity and low contrast between different phases. The problem becomes even more severe when thick specimens need to be investigated, a situation that is common for materials that are ordered from the nanometer to micrometer length scales or when performing dynamic experiments in a TEM liquid cell. Here we report a method to optimize annular dark-field (ADF) STEM imaging conditions and detector geometries for thick and beam-sensitive low-contrast specimen using the example of a carbon nanotube/polymer nanocomposite. We carried-out Monte Carlo simulations as well as quantitative ADF-STEM imaging experiments to predict and verify optimum contrast conditions. The presented method is general, can be easily adapted to other beam-sensitive and/or low-contrast materials, as shown for a polymer vesicle within a TEM liquid-cell, and can act as an expert guide on whether an experiment is feasible and to determine the best imaging conditions.