Widespread application of magnetic tunnel junctions (MTJs) for information storage has so far been limited by the complicated interplay between tunnel magnetoresistance (TMR) ratio and the product of resistance and junction area (RA). An intricate connection exists between TMR ratio, RA value and the bandgap and crystal structure of the barrier, a connection that must be unravelled to optimise device performance and enable further applications to be developed. Here, we demonstrate a novel method to tailor the bandgap of an ultrathin, epitaxial Zn-doped MgO tunnel barrier with rocksalt structure. This structure is attractive due to its good Δ1 spin filtering effect, and we show that MTJs based on tunable MgZnO barriers allow effective balancing of TMR ratio and RA value. In this way spin-dependent transport properties can be controlled, a key challenge for the development of spintronic devices.