Buffers find application in a wide range of contexts, from digital hardware and software systems to broadband packet-switched networks like the Internet. Traditionally, such buffers are designed without regard for the characteristics of the content they will hold. For example, with a simple first-in/first-out (FIFO) buffer, if during some interval of time the number of bits that needs to be stored exceeds the memory resources, some are simply dropped. When those bits represent some multimedia content of interest, the dropped bits correspond to a loss of fidelity. In this work, we examine the design of a smart buffer that takes into account how each bit contributes to the fidelity of the content stored in memory, and develop a buffering algorithm that optimizes end-to-end fidelity. In particular, we develop a greedy algorithm is sample-path optimal: regardless of the pattern of arrivals to and departures from memory, no other algorithm, greedy or not, can achieve better performance. This algorithm ensures that most-significant bits are both stored in memory first and depart memory first, with the resource allocation managed by an easily implemented waterpouring strategy. The smart buffer achieves a given end-to-end fidelity target with considerably less storage and communication resources than traditional designs. From a system or network architecture perspective, the resulting design shows how increasing lower layer awareness of the application layer in relatively simple ways can substantially improve resource efficiency.