We study the problem of personalized, interactive tag recommendation for Flickr: While a user enters/selects new tags for a particular picture, the system suggests related tags to her, based on the tags that she or other people have used in the past along with (some of) the tags already entered. The suggested tags are dynamically updated with every additional tag entered/selected. We describe a new algorithm, called Hybrid, which can be applied to this problem, and show that it outperforms previous algorithms. It has only a single tunable parameter, which we found to be very robust. Apart from this new algorithm and its detailed analysis, our main contributions are (i) a clean methodology which leads to conservative performance estimates, (ii) showing how classical classification algorithms can be applied to this problem, (iii) introducing a new cost measure, which captures the effort of the whole tagging process, (iv) clearly identifying, when purely local schemes (using only a user's tagging history) can or cannot be improved by global schemes (using everybody's tagging history).