  Narrow sieves, representative sets and divide-and-color are three
breakthrough color coding-related techniques, which led to the design of
extremely fast parameterized algorithms. We present a novel family of
strategies for applying mixtures of them. This includes: (a) a mix of
representative sets and narrow sieves; (b) a faster computation of
representative sets under certain separateness conditions, mixed with
divide-and-color and a new technique, "balanced cutting"; (c) two mixtures of
representative sets, iterative compression and a new technique, "unbalanced
cutting". We demonstrate our strategies by obtaining, among other results,
significantly faster algorithms for $k$-Internal Out-Branching and Weighted
3-Set $k$-Packing, and a framework for speeding-up the previous best
deterministic algorithms for $k$-Path, $k$-Tree, $r$-Dimensional $k$-Matching,
Graph Motif and Partial Cover.
