Despite the considerable growth of Information Systems (IS) outsourcing in recent years, this trend is still the object of strong criticism. This study has as its aim to show the main risks computer outsourcing entails for the largest Spanish firms. In order to achieve that aim, we have reviewed the previous literature on this topic and later analysed the results of a survey covering 5,000 firms. According to the firms under analysis, the main concern in relation to IS outsourcing is the excessive dependence on the provider this type of contract may generate. Nevertheless, some characteristics of firms (mainly their size) somehow determine what risks are seen as the most relevant. The conclusions also suggest that total outsourcing can turn out to be a very dangerous strategy, mainly due to the dependence it creates. This is why IS managers should consider other alternatives such as having multiple providers or resorting to selective outsourcing.