RegretNet is a recent breakthrough in the automated design of revenue-maximizing auctions. It combines the flexibility of deep learning with the regret-based approach to relax the Incentive Compatibility (IC) constraint (that participants prefer to bid truthfully) in order to approximate optimal auctions. We propose two independent improvements of RegretNet. The first is a neural architecture denoted as RegretFormer that is based on attention layers. The second is a loss function that requires explicit specification of an acceptable IC violation denoted as regret budget. We investigate both modifications in an extensive experimental study that includes settings with constant and inconstant numbers of items and participants, as well as novel validation procedures tailored to regret-based approaches. We find that RegretFormer consistently outperforms RegretNet in revenue (i.e. is optimal-er) and that our loss function both simplifies hyperparameter tuning and allows to unambiguously control the revenue-regret trade-off by selecting the regret budget.