We study the physics reach of the long-baseline oscillation analysis of the DUNE experiment when realistic simulations are used to estimate its neutrino energy reconstruction capabilities. Our studies indicate that significant improvements in energy resolution compared to what is customarily assumed are plausible. This improved energy resolution can increase the sensitivity to leptonic CP violation in two ways. On the one hand, the CP-violating term in the oscillation probability has a characteristic energy dependence that can be better reproduced. On the other hand, the second oscillation maximum, especially sensitive to $delta_{CP}$, is better reconstructed. These effects lead to a significant improvement in the fraction of values of $delta_{CP}$ for which a $5 sigma$ discovery of leptonic CP-violation would be possible. The precision of the $delta_{CP}$ measurement could also be greatly enhanced, with a reduction of the maximum uncertainties from $26^circ$ to $18^circ$ for a 300~MW$cdot$kt$cdot$yr exposure. We therefore believe that this potential gain in physics reach merits further investigations of the detector performance achievable in DUNE.
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