Bright sources of mega-electron volt (MeV) x-rays have many unique applications, including nuclear physics, radiation oncology, and imaging high areal density systems. High intensity lasers (> 1018 W cm−2) incident on mm-thick metal targets can deliver MeV x-rays via the bremsstrahlung process, providing sources with ultrashort duration ( ∼ps) and small source size (∼100  μm). Here, we report on a reproducible regime of laser-driven MeV x-ray sources, where the x-ray dose can be further increased by 60% by coating the metal target with micrometers of plastic. High fidelity numerical simulations indicate that the interaction is a result of relativistic transparency in the preplasma. Though relativistic transparency is present in both cases, the greater sound speed and smaller ion inertia of the plastic target allow the laser to more deeply penetrate and couple more efficiently to electrons. Radiography with this system demonstrates a resolving power < 300  μm, important for imaging applications.