We consider a noncanonical ensemble which involves a sample thermally connected to a finite heat bath with specific properties. Treating the size of the heat bath as a parameter, we show that static properties of finite samples are ensemble dependent. Monte Carlo simulations of phase transitions in Potts models confirm the analysis and demonstrate significant reductions in computer time (sometimes by a factor of 100) compared to canonical-ensemble simulations. For finite samples, second-order transitions are sharpened and are clearly distinguished from first-order transitions as the heat bath becomes smaller.