An individual experiences double coverage when he bene ts from more than one health insurance plan at the same time. This paper examines the impact of such supplementary insurance on the demand for health care services. Its novelty is that within the context of count data modelling and without imposing restrictive parametric assumptions, the analysis is carried out for di¤erent points of the conditional distribution, not only for its mean location. Results indicate that moral hazard is present across the whole outcome distribution for both public and private second layers of health insurance coverage but with greater magnitude in the latter group. By looking at di¤erent points we unveil that stronger double coverage e¤ects are smaller for high levels of usage. We use data for Portugal, taking advantage of particular features of the public and private protection schemes on top of the statutory National Health Service. By exploring the last Portuguese Health Survey, we were able to evaluate their impacts on the consumption of doctor visits.