We study the design of public long-term care (LTC) insurance when the altruism of informal caregivers (children) is uncertain. The original feature of our analysis is that we consider nonlinear policies linking the public LTC transfer to the level of informal care, assuming that the latter is observable but children's altruism is not. The traditional topping up and opting out policies are special cases of ours. Since none of these schemes appears to systematically dominate the other, one does not expect our problem to yield any of these extreme solutions. Interestingly, however, we do not find intermediate solutions either. The optimal social LTC transfer need not be decreasing with the level of informal care provided, in order to provide incentives to caregivers. Both total and informal care should increase with the children's level of altruism. This obtains under full and asymmetric information. Social LTC, on the other hand, may be non-monotonic. Our examples suggest that, under full information, while the optimal LTC transfer may first be increasing in the children's level of altruism, it should decrease for larger levels and eventually drop to zero. Under asymmetric information, social LTC is lower than its full information level for the lowest level of altruism, while it is distorted upward for the higher level of altruism. This is explained by the need to provide incentives to high-altruism children. The implementing contract is always such that social care increases with informal care.