We examine the effects of market making and intermittent trading on estimates of stock price volatility. When observed price changes are correctly tied to a stock's true price dynamics, it is found that non-trading per se causes a loss of efficiency but no bias in traditional volatility estimates. Non-trading induces substancial inefficiency in the extreme value estimator of volatility which it biases downward. Market making's effects add to the non-trading induced inefficiency in the traditional estimator, while information trading causes a downward bias, and liquidity trading a potentially removable upward bias, in that estimator.