We present a complete redesign of Evaluation Strategies, a key abstraction for specifying pure, deterministic parallelism in Haskell. Our new formulation preserves the compositionality and modularity benefits of the original, while providing significant new benefits. First, we introduce an evaluation-order monad to provide clearer, more generic, and more efficient specification of parallel evaluation. Secondly, the new formulation resolves a subtle space management issue with the original strategies, allowing parallelism (sparks) to be preserved while reclaiming heap associated with superfluous parallelism. Related to this, the new formulation provides far better support for speculative parallelism as the garbage collector now prunes unneeded speculation. Finally, the new formulation provides improved compositionality: we can directly express parallelism embedded within lazy data structures, producing more compositional strategies, and our basic strategies are parametric in the coordination combinator, facilitating a richer set of parallelism combinators. We give measurements over a range of benchmarks demonstrating that the runtime overheads of the new formulation relative to the original are low, and the new strategies even yield slightly better speedups on average than the original strategies.