We propose a new formulation of the index coding problem, where instead of demanding a specific message, clients are “pliable” and are happy to receive any one message they do not have. We prove that with this relaxation, although some instances of this problem become simple, in general the problem remains NP-hard. However, we develop heuristic algorithms that in our (extensive) experimental evaluation required only a logarithmic (in the number of messages) number of broadcast transmissions; this is an exponential improvement over tradi- tional index coding requirements.