because the listing agent made it seem like he was not in a hurry.My initial offer got rejected and I'm trying to structure a counter-offer with an incentive to the seller without bringing up the original offer price too much.

In OR, you can not reject an app based on source of income. 

It will be good to have as evidence if you are ever questioned about fair housing, you can show that you have credit reports and applicants you approved have better reports than the ones you rejected.

One strategy I've found that works sometimes is, even if your initial offer is rejected, keep following the property you like after its status is changed to Pending.

I put my first bid in and it was rejected with no counteroffer.

Also never give a reason for rejecting any applicant aside from  possible saying you accepted a more qualified applicant.

If full-time RE investors are already rejecting the industrial-age game of life with the prescribed formula of 'college-->job-->family-->house-->retire', then shall I likewise reject the mantra "Play to win" and make my own rules for the game of RE investing?  

By the next day I had an email from the lender cancelling there rejection of the previous offer and requesting I send out a new one with a close date within 30 days.

I have (nicely) rejected two applicants that I can remember.

I know there are some restrictions on what FHA  rejects as a property to finance and was curious if anyone knew the restrictions of foundation settling.