If integrity is in question it should be a two way street.When buyers put in highest and best offers and agent comes back looking for more if we assume buyers have integrity there would be no counter offers.

Sounds like you've dealt with HUD properties before.On Tuesday (March 19th) the property will have been on the market for 56 Days (8 Weeks).Do you know if HUD Counteroffers at all?

The first offer was my original offer for the 950000 and the second was the agent of the owner with the counteroffer which I will send a counter tomorrow.  

That 3 other people had put bids in, and we should expect a counter offer soon.

Negotiate all offers and counteroffers on seller(s)’ behalf.124.

I made an offer and by the time the came back to me with a counter offer (about a week later), I was already under contract with a different home.

An interesting piece of information is that they pulled in all the dates along with closing date in their counter offer and even called my bank to see how quickly I could close. 

They may reject entire offer; they may also make a counter offer somewhere in the middle.

I signed their counteroffer one week ago today.

Tie it up in contract with an X day inspection contingency.On day X-1, I'd submit my counteroffer that includes two things and one alternative:- Whatever I want to negotiate on, re: inspection results.