Both single-layer and multilayer imageable elements have a substrate and at least one imageable layer. The elements can be used to prepare either negative- or positive-working imaged elements, for example as lithographic printing plates. The imageable elements also include a radiation absorbing compound and a solvent-resistant polymer comprising pendant phosphoric acid groups, pendant adamantyl groups, or both. When this polymer comprises pendant adamantyl groups, they are connected to the polymer backbone through a urea or urethane group. The imageable elements have improved chemical resistance and thermal bakeability from the presence of the unique solvent-resistant polymer.