This is where the estate agent often ends up working for the purchaser, against his own client. By giving the estate agent a signed contract you also give him a "conditioning tool".
The estate agent will use your signed contract to convince the vendor that the market is talking, and that the price you have offered in hard copy is about the best he can expect to get. Remember, the estate agent will miss out on a commission unless he can get a sale, any sale, at any price, during the currency of his agency contract with the vendor. Thus, time is the enemy for the estate agent.
If you make a written offer, with a time limit of say two days, and you present as unwavering in your determination not to go any higher in price, the estate agent will turn on his own client. I have seen this happen time and time again.
A word of warning however - you must remain firm to use the estate agent in this way, as agents are very good at identifying the weaker party and their ability to keep the parties separated leaves plenty of room for lies and other forms of deception.