diff --git a/protocol.go b/protocol.go
index 1cdf10f..7bbb8e5 100644
--- a/protocol.go
+++ b/protocol.go
@@ -134,8 +134,13 @@ func (p *Listener) Addr() net.Addr {
 // NewConn is used to wrap a net.Conn that may be speaking
 // the proxy protocol into a proxyproto.Conn
 func NewConn(conn net.Conn, opts ...func(*Conn)) *Conn {
+	// For v1 the header length is at most 108 bytes.
+	// For v2 the header length is at most 52 bytes plus the length of the TLVs.
+	// We use 256 bytes to be safe.
+	const bufSize = 256
+
 	pConn := &Conn{
-		bufReader: bufio.NewReader(conn),
+		bufReader: bufio.NewReaderSize(conn, bufSize),
 		conn:      conn,
 	}