We report on dispersion management in mid-IR optical parametric chirped pulse amplifiers (OPCPA) aiming for high-energy few-cycle pulses beyond 4 µm. The available pulse shapers in this spectral region limit the feasibility of sufficient higher-order phase control. Intending the generation of high energy pulses at 12 µm via DFG driven by the signal and idler pulses of a midwave-IR OPCPA, we introduce alternative approaches for mid-IR pulse shaping, namely a germanium-prism pair and a sapphire-prism Martinez compressor. Furthermore, we explore the limits of bulk compression in Si and Ge for multi-mJ pulse energies.