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Recent years have seen a large number of proposals for anonymity mechanisms operating on the application layer. Given that anonymity is no stronger than its weakest link, such proposals are only meaningful if one can offer anonymity guarantees on the communication layer as well. ANODR - or anonymous on demand routing - is one of the leading proposals to deal with this issue. In this paper, we propose a novel technique to address the same problem, but at a lower cost. Our proposal, which we dub discount-ANODR, is built around the same set of techniques as ANODR is. Our proposal has the benefit of achieving substantially lower computation and communication complexities at the cost of a slight reduction of privacy guarantees. In particular, discount-ANODR achieves source anonymity and routing privacy. A route is "blindly generated" by the intermediaries on the path between an anonymous source and an identified destination. Route requests in discount-ANODR bear strong similarities to route requests in existing source routing protocols, with the limitation that intermediaries only know the destination of the request and the identity of the previous intermediary - but not whether the latter was the originator of the request. The response to a route request protects the compiled route by means of iterated symmetric encryption, drawing on how messages are prepared before being submitted to a typical synchronous mix network (or onion router). The communication of data subsequently uses such "route onions" to channel the packet to the intended destination. We do not use any key exchange, nor do we utilize public key operations at any time; consequently, we do not need to rely on any PKI, CRL or related constructions