During the past ten years or so, trading in financial markets has become increasingly automated, with recent estimates suggesting that high frequency trading (HFT) now accounts for more than half of all transactions in US equity markets. This has given rise to a debate among academics, practitioners and regulators about the benefits and concerns associated with an increasing automation of the trading process. This paper contributes to this debate representing a stylized model of trading in a limit order market where agents differ in their trading speed which is thought to capture the difference between (fast) HFT and slow human market participants. The paper argues that proposed regulatory changes such as limits on order cancellations or minimum order resting times are likely to lead to optimum outcome because they precisely address the source of potential efficiency gains derived from HFT. The taxation of HFT high frequency activity may improve upon rules that lead this type of activity to disappear completely.