My philosophy is simple: If you’d be bummed-out to lose it over a few thousand dollars you were willing and able to pay anyway, don’t screw around holding it back. Put your best reasonable offer forward and give yourself the best chance to win. A highly competitive market is usually not the place to play games.
And yes, no appraisal contingency, large EMD and short time frames.

In a competitive market, I advise my client to write only one offer....the best, most attractive offer that they can make. If someone else writes a better, more compelling offer, my client knows that they tried their best.

If you REALLY WANT THAT home you may want to consider the asking price and offering it. They are going fast.

I ask questions to clear the air.

1. How bad do you want this property

2. If you don't get it, can you move on?

3. Will you waive repairs to get it?

Offer after the buy formula is worked out plus or minus & keep it fair. If rejected or not countered, you are free to move on to the next dream

A very large EMD.  Money talks!

 Contingencies?   As few as possible, and definitely line out the Appraisal contingency. 

I never advised buyers to remove any contingencies. Make your offer the strongest you want to with $$ and inline with the likely value, and be prepared to lose. 

You're so right on the appraisal waiver, Tony! In NC, depending upon the condition of the property, a very high Due Diligence Fee (DDF) often helps. The DDF is very similar to an Option Fee with regards to land and commercial deals. 

Do you want to purchase a house or not? If not then don't waste a lot of peoples time. If you really want to purchase a house you need to be competitive in a competitive market. The Clash said it best: "Should I Stay Or Should I Go?"

IN a highly competitive market my suggestion is offering your highest and best the first time around. Not enough? Walk or cough Iup more. Some will and some won't. Their choice. A few thousand should never kill a deal. 

Bring the absolute best foot forward.  To quote The Godfather, make them an offer they can't refuse.

I agree with many of the comments here.  Give it your best shot - go all in.  

In my market - we are not talking about a couple thousand dollars - it can be $50,000 - $100,000 or more above the list price. Waiving the appraisal and other contingencies is also common in my market. 

Depends on the buyers' situation - how high they might want to go or how much risk they are willing to bear. One time, in a super insanely competitive market, after almost two years of looking and missing out, when the "right" home came along, my advice was "go for broke"! It was a family member. They put in an offer that was a good chunk over asking (but doable based on careful income/cost calculations), got the house without going back and forth and are VERY happy there. I worked hard to make sure home appraised, digging through microfiche records in the town building department to research original blueprints, updates, etc. It appraised!

Have your REBNY Financials complete early so that I can calculate my buyer's DTI and Post Closing Liquidity. Also, I want a full profile - i.e. primary residence, pied a terre, etc. Pets- and if yes, breeds, size/weight, Attorney's name/contact info, etc. Anything I can share that might have value- i.e. do you have friends or family in the building? Does the buyer already have pre-existing relationships to the community, etc. , when does the buyer want to close (the buyer might have limited control over this issue- but I often advise within 2 weeks of board approval). 

There are a lot of answers in this thread that don't apply to my market or often doesn't apply. I suspect others will respond that accordingly that what I wrote doesn't apply to their market. 

When I write an offer, I have often heard (even for my market) that my offer is well organized and robust info- and I know from past experience that alone can help me win my clients the apartment in a competitive environment. Price and bidding more isn't always the right answer here- especially in co-op's where the buyer has to meet or exceed a high bar of requirements- so the highest bid might not win. 

EMD's here are typically 10%  - which may be higher than other agents suggest on this feed- but on this point I am not sure. 

I explain all the risks and ask the buyer how much they want to own the property, and suggest that they make their best offer.  If they want to lowball I do pause and ask them if they really are not serious about this one.  Most will reconsider if they really want it.