Algebraic effect handlers are becoming an increasingly popular way of structuring effectful computations, and their performance is often a concern. One of the proposed approaches towards efficient compilation is tracking effect information through explicit subtyping coercions. However, in the presence of polymorphism, these coercions are compiled into additional arguments of compiled functions, incurring significant overhead. In this paper, we present a polymorphic effectful calculus, identify simplification phases needed to reduce the number of unnecessary constraints, and prove that they preserve semantics. In addition, we implement the simplification algorithm in the Eff language and evaluate its performance on a number of benchmarks. Though we do not prove the optimality of the presented simplifications, the results show that the algorithm eliminates all coercions, resulting in code as efficient as manually monomorphised one.