Data mining and profiling offer great opportunities, but also involve risks related to privacy and discrimination. Both problems are often addressed by implementing data minimization principles, which entail restrictions on gathering, processing and using data. Although data minimization can sometimes help to minimize the scale of damage that may take place in relation to privacy and discrimination, for example when a data leak occurs or when data are being misused, it has several disadvantages as well. Firstly, the dataset loses a rather large part of its value when personal and sensitive data are filtered from it. Secondly, by deleting these data, the context in which the data were gathered and had a certain meaning is lost. This chapter will argue that this loss of contextuality, which is inherent to data mining as such but is aggravated by the use of data minimization principles, gives rise to or aggravates already existing privacy and discrimination problems. Thus, an opposite approach is suggested, namely that of data minimummization, which requires a minimum set of data being gathered, stored and clustered when used in practice. This chapter argues that if the data minimummization principle is not realized, this may lead to quite some inconveniences; on the other hand, if the principle is realized, new techniques can be developed that rely on the context of the data, which may provide for innovative solutions. However, this is far from a solved problem and it requires further research.