With the HttpURLConnection API, use `setChunkedStreamingMode(0)` to avoid buffering the post body. The [docs](http://developer.android.com/reference/java/net/HttpURLConnection.html) call this out:

> To upload data to a web server, configure the connection for output using setDoOutput(true).
For best performance, you should call either setFixedLengthStreamingMode(int) when the body length is known in advance, or setChunkedStreamingMode(int) when it is not. Otherwise HttpURLConnection will be forced to buffer the complete request body in memory before it is transmitted, wasting (and possibly exhausting) heap and increasing latency.

For the Request/Response API, the body is never buffered. I need to update those docs.