First, determine the real value of the property. Second, if you've been pre-approved or pre-qualified, take that number. Third, determine how much you can comfortably afford to spend, which may well be less than your pre-approved/pre-qualified amount.
Take the lowest of those three numbers (value, pre-qualification amount, affordability amount). That's the most--the MOST--you should spend for the property.
Notice we haven't even discussed the listed price of the house? That's because it has nothing to do with the house's value, what you're qualified for, or what you can comfortably spend.
Now you can look at the listing price. Take the listing price and the number you came up with above as the most you can spend. Take the lower of those two numbers. That's your new maximum limit. If the owner's asking for less than the value, less than you're pre-qualified for, and less than you're comfortable spending, then you lower your offer to the listing price.
But never, ever, raise your offer if your own low number (value, pre-qualification, comfort level) is below the listing price.
And these calculations apply whether you're in Purvis, Mississippi or San Francisco.
Do not worry about insulting a seller. Worry about value and your ability to afford the property.
1) Decline with no counter offer
2) Counter offer
As Ms.Starnes pointed out, see how long the property has been on the market. If the property has been on the market an abnormal period of time, then this might justify the drop in the offering price. Even if the owner does not accept the price, might as well test the waters and attempt and see if he comes with a counteroffer. Then work around the counter to you reach a mutually beneficial agreement. If you feel as if the property is not worthwhile at this price bracket (after searching the true comparables), then move on.
But at least attempt.
Remember, as you are submitting an offer, you never can tell who is right behind you with a better offer and better qualifications ( Even the all cash types). Even when an offer is accepted, the owner still could accept another offer. Words and not binding. Fully executed contacts are. The name of the game is to have the attorney, mortgage banker all in your pocket, so when you are ready to pull the trigger, you can get to the contract ASAP. Best wishes with your endeavors.
The best advice is this: If you really want the house, make your offer but be prepared to raise your offer. If you are willing to walk away, you haven't lost anything in trying.