As for all health systems, in Russia, the demand for medical care is greater than its health system is able to guarantee the supply of. In this context, removing services from the state guaranteed package is an option that is receiving serious consideration. In this paper, we examine the attitudes of the Russian population to such a reform. Exploiting a widely-used methodology, we explore the population's willingness to pay for cooperative health insurance. Distinguishing between socioeconomic and demographic factors, health-related indicators and risk aversion we find, consistent with other literature, positive income and risk aversion effects. We interpret the former as evidence that the Russian population is not opposed to the idea of progressive redistribution, to pool the costs of health-related risks; and the latter as evidence that risk-averse individuals demand more insurance coverage. In exploring these results further, we show that cognitive bias is important: overestimating the benefits leads to the purchase of additional insurance, while underestimating lowers demand for insurance. Our overall conclusion is that the introduction of a supplementary cooperative health insurance scheme in Russia could increase the accessibility of healthcare, lower the tendency for informal payments, incentivize the personal maintenance of good health and create a new source of funding for public healthcare.