Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain the following results: 1. Better randomized algorithms for unfair metrical task systems on the uniform metric space. 2. Better randomized algorithms for metrical task systems on general metric spaces, O(log2 n(log log n)2) competitive, improving on the best previous result of O(log5 n log log n). 3. A tight randomized competitive ratio for the k-weighted caching problem on k+1 points, O(log k), improving on the best previous result of O(log2 k).