There are many psychological influences that affect our ability to sometimes negotiate in our own best interests. Check your own thought processes to see whether you are being negatively impacted by any of the following:
Reactive Devaluation: Things that are offered are less valuable than things that are not offered. Since people value offers based on the source of the offer, get them to think that they came up with the offer.
Naive Realism and Projection: People believe they "see the world as it is" and that others think the way they do. This causes them to give too much weight to information that confirms what they already believe and undervalue information that contradicts what they already believe. Therefore, before going into a negotiation, have others review to clarify your critical thinking or use a neutral to test reality of all parties.