Oddly enough though if I have adequately "aged" UTXOs I can send txs (that involve a large enough BTC amount) with *no fee* and they will appear generally in the very next block!
priority = sum(input_value_in_base_units * input_age)/size_in_bytes (source:
https://en.bitcoin.it/wiki/Transaction_fees#Technical_info)
Input age (number of confirmations) and number of coins sent have a huge affect on transaction priority. (assuming the pools haven't changed the relevant settings too much.)