We investigate the implementation of multi-label classification algorithms with a reject option, as a mean to reduce the time required to human annotators and to attain a higher classification accuracy on automatically classified samples than the one which can be obtained without a reject option. Based on a recently proposed model of manual annotation time, we identify two approaches to implement a reject option, related to the two main manual annotation methods: browsing and tagging. In this paper we focus on the approach suitable to tagging, which consists in withholding either all or none of the category assignments of a given sample. We develop classification reliability measures to decide whether rejecting or not a sample, aimed at maximising classification accuracy on non-rejected ones. We finally evaluate the trade-off between classification accuracy and rejection rate that can be attained by our method, on three benchmark data sets related to text categorisation and image annotation tasks.