Charles Dominick recently wrote this brief article about what vendors fear, you can read more about this by following the link at the bottom. I am sure you have using these fears to your advantage at some point or the other in your negotiations
Losing to a competitors: well, this is obvious. The suppliers always fear losing business to other competitors. Putting an RFP out is one way to ensure that vendors are aware that they are not the only one bidding for your business. A well defined process will also ensure that vendors know what to expect. For example, The RFP is sent to 5 vendors, Shortlist will be top 3 and selection will be from Top 2.
Potential of project being killed due to budget: Most of the times suppliers lose business because either Buying organization decide to do nothing or the cost of the project is over the budgeted amount. Letting vendors know that the project might get killed if they don’t reduce the price might work to your advantage.
Failing to get their “foot in the door”: Vendors are always trying to get their foot in the door either to replace to incumbent or get some share of the existing business. You can use that to your benefit if positioned well to the vendor along with the long term prospect.
Reputation loss: Vendors fear losing their face if they give a very high price earlier, got eliminated and then try to win your business by reducing the price. That is not good the vendor and for their reputation. A clear communication to the vendors stating that if they are eliminated they will not be entertained can go a long way to ensure that vendors put their best foot forward.