This paper studies wholesale electricity markets where an exogenous price cap is enforced, compromising both short- and long-term incentives. To guarantee capacity adequacy, policy-makers may provide support for generation through a capacity remuneration mechanism (CRM) and/or encourage demand response (DR). Such mechanisms are formalised within a common simple analytical framework, clarifying how these mechanisms relate to each other. We then divide them into two categories, depending on whether their implementation requires transactions to be made based explicitly on spot prices higher than the price cap. While mechanisms that keep implicit these high marginal costs are likely to be preferred from a political perspective, they also appear to be less efficient. If they are to be implemented nonetheless, we suggest that the price cap should be set higher than the marginal cost of the most expensive plant, and highlight that challenges for demand-response integration in CRMs remain.