The 2013 MINI Cooper family hasn't earned safety ratings that are all that impressive. But with a reasonably good set of safety equipment and excellent handling--with which you might avoid accidents--you shouldn't disqualify these models on safety alone.
The Cooper and Cooper S earn the Insurance Institute for Highway Safety (IIHS) rating of "good" in front-impact crash testing, but only "acceptable" in side impacts. Roof strength likewise receives an "acceptable" score. The MINI Cooper hasn't been tested by the federal government, but it does earn a five-star rollover resistance rating.
But what makes the MINI Cooper a safer bet than it might sound, given its diminutive size and ratings, is a good set of features. Six airbags, anti-lock brakes, stability control, and hill-start assist are all standard, and options that may aid safety include xenon headlamps and parking sensors.