Automatic speaker verification (ASV) systems are vulnerable to spoofing attacks. We propose a spoofing-robust ASV system optimized directly for the recently introduced architecture-agnostic detection cost function (a-DCF), which allows targeting a desired trade-off between the contradicting aims of user convenience and robustness to spoofing. We combine a-DCF and binary cross-entropy (BCE) with a novel straightforward threshold optimization technique. Our results with an embedding fusion system on ASVspoof2019 data demonstrate relative improvement of $13\%$ over a system trained using BCE only (from minimum a-DCF of $0.1445$ to $0.1254$). Using an alternative non-linear score fusion approach provides relative improvement of $43\%$ (from minimum a-DCF of $0.0508$ to $0.0289$).