(joint work with Shane Mansfield) As it is usually presented, the physical consequence of contextuality is that it forces one to give upon either determinism or parameter-independence. The latter ensures that measurement responses are independent of context, i.e. any other compatible measurements that are performed jointly. These are assumptions that apply to hidden variable models, which are supposed to encompass any reasonable physical description that could underlie the empirical data. In realistic, noisy experiments however, the validity of those assumptions can be called into question. This introduces loopholes to the physical conclusions one can draw from instance of contextuality. A number of previous works have addressed one or other of these loopholes. We build on this to provide a unified approach to closing both loopholes by introducing appropriate correction terms to the contextual fraction measure of contextuality.