With reference to the newly emerging climate finance architecture under the post-Kyoto framework, this paper argues that a stronger focus must be placed on how the funds are to be spent in the recipient countries according to different needs, an issue we call the 'mode of funding'. We make our points based on a noncooperative two-country framework in which an industrialized and a developing country decide on mitigation in the first stage and on adaptation in the second stage of the game. The funding instruments recently agreed upon in UN climate negotiations are modeled in a stylized manner that highlights their specific modes of funding, such as tying the industrialized countries' transfer payments to a reduction in the developing countries' potential or actual loss and damages, mitigation or adaptation costs. We show that the various modes of funding may give rise to strategic choices when it comes to the countries' mitigation efforts. Moreover, some such modes (compensation for actual loss and damages and for adaptation costs) fall short of two essential minimum requirements for enabling Pareto improvements for donor and recipient alike and thus cannot guarantee sustained voluntary funding. We also demonstrate that the presumed equivalence of sequencing the decision on mitigation before adaptation compared to deciding simultaneously on mitigation and adaptation does not hold if different modes of climate funding are considered.