The growth of real-time content streaming over the Internet has resulted in
the use of peer-to-peer (P2P) approaches for scalable content delivery. In such
P2P streaming systems, each peer maintains a playout buffer of content chunks
which it attempts to fill by contacting other peers in the network. The
objective is to ensure that the chunk to be played out is available with high
probability while keeping the buffer size small. Given that a particular peer
has been selected, a \emph{policy} is a rule that suggests which chunks should
be requested by the peer from other peers.. We consider consider a number of
recently suggested policies consistent with buffer minimization for a given
target of skip free playout. We first study a \emph{rarest-first} policy that
attempts to obtain chunks farthest from playout, and a \emph{greedy} policy
that attempts to obtain chunks nearest to playout. We show that they both have
similar buffer scalings (as a function of the number of peers of target
probability of skip-free probability). We then study a hybrid policy which
achieves order sense improvements over both policies and can achieve order
optimal performance. We validate our results using simulations.