"Mentioning those rival products"
The trick here is identifying the products arch-nemesis, they always have at least one.. Sometimes vendors are so desperate for market share (rather than profit) that they will sell at a loss, just to win the business... don't think this only applies to multi-million pound purchases (This is possible even for SME's, if you do it at the right time).
The downside though, this can get stressful.. as not only are you playing chicken with the vendor, you are also fighting to get the purchase signed off internally a lot quicker than you normally would..