Automatic speaker verification (ASV) systems are vulnerable to spoofing attacks such as text-to-speech. In this study, we propose a novel spoofing-robust ASV back-end classifier, optimized directly for the recently introduced, architecture-agnostic detection cost function (a-DCF). We combine a-DCF and binary cross-entropy (BCE) losses to optimize the network weights, combined by a novel, straightforward detection threshold optimization technique. Experiments on the ASVspoof2019 database demonstrate considerable improvement over the baseline optimized using BCE only (from minimum a-DCF of 0.1445 to 0.1254), representing 13% relative improvement. These initial promising results demonstrate that it is possible to adjust an ASV system to find appropriate balance across the contradicting aims of user convenience and security against adversaries.