Why would you want your appraisal to come in higher when you are buying a house? If your appraisal came in $10,000 lower, buy the house for $10,000 less. We always write into the purchase agreement that we will pay xxx or the appraised price, which ever is lower. We have been in situations where appraisals have come back significantly lower and this takes care of the issue.
After we went under contract, our realtor got the impression that the sellers were feeling "seller's remorse." If we went back to renegotiate the price, our realtor, who is not only a close friend, but in the business for over 20 years felt that they would prefer the contract to fall apart at that point. They aren't in a forced move for job, they aren't underwater, or anything like that. They are having to move into a rental because they can't find a house they like.
And our realtor had legitimate concerns with the comps the appraiser used. The house we are buying is on a cul-de-sac in the middle of a subdivision, and 2 of the comps that were used were for houses backing onto a major 4 lane road. The area where we are buying has had limited sales in the period the appraiser could look at. The house is on a lot that is significantly larger than anything that has sold, and there were questions about if the adjustment to account for that was adequate. Two additional properties closed after his initial pull. We asked him to consider those. It was after that, that he adjusted his appraisal up $6K. Which brought the appraised value to more than the list price of the house. The difference was our closing costs we rolled into the loan. We had wanted to preserve cash, although it's probably better that we are just paying them up front anyway.
Aside from those reasons, after looking at dozens of houses, this house was by far in the best condition than anything else we had considered. The other houses, would have come with major cosmetic updates (kitchen, baths, carpets). This house had the proper permits filed with the city for the basement renovation and deck, and the inspector could tell from what he could see it was a high quality professional job. It's a 40 year old house and the inspector could not come up with anything of concern, and called it a "gem of a house." The appraiser isn't looking at those things. Given a choice between having to come up with an extra $4K in cash because of a low appraisal, and knowing that we aren't going to have to sink money into replacing carpets, stripping wallpaper, replacing circa 72 kitchen cabinets and appliances, and harvest gold sinks and tubs in a house that appraised out...well, you can see which one we chose.
If the difference had been greater, certainly things would have been different. If we knew the seller had to sell, and it would be difficult for them to find another buyer (we were under contract about 36 hours after the house was listed and they had multiple offers), that would have made a difference in negotiating.
But the point I was making by posting originally, is that a slightly low appraisal is not the end of the world. Make sure the appraiser did his job.