A computer-implemented method, in different embodiments, is provided to construct on-line payments without resorting to aggregation. The embodiments permit smaller total fees, permit the intermediary payment system to intermediate payments without holding third-party funds, and permit eliminating or reducing chargeback liability. In one embodiment, an intermediary payment system maintains records of unpaid amounts for potential receivers, and determines one or more potential receivers, but not all of them, to become effective receivers of a nominal amount. The primary payment system transfers amounts from the user and to receivers. The intermediary payment system reduces records of unpaid amounts for effective receiver, and raises records of unpaid amounts for potential receivers.