This paper concerns a decision problem of an agent, searching to find a low price, whose memory is represented by a partition of the set of possible past prices. The number of elements in the partition is limited. I characterize the optimal partition for the case of a single decision, and then consider memory allocation among several decisions. I consider a case in which a consumer who must allocate a single bit of memory among two decision problems would do better to allocate it exclusively to one of the problems than to use it to convey joint information about both.