Most agents will agree on one thing: All the personal touches in the world don’t matter if the offer isn’t strong.

It’s the dirty little secret in real estate that brokers tend to admit only in the company of one another: When it comes to winning a seller over, a buyer’s personality matters.

“This whole thing with buyers and sellers is a dance of romance,” says Steven James, president and CEO of Berkshire Hathaway HomeServices New York. “Honestly in some of these situations, it’s not about the money—it’s about emotion.”

When buyers expect they’ll be competing against multiple other offers, there are some ways that they can make a personal impact on sellers—and their agents—to win them over.

While most agents say they advise sellers to leave personality aside and focus on the price and terms of an offer, some admit to subtly advocating on behalf of buyers that left an impression on them.

“They really are biased, whether they know it or not,” said Lori Abbey, a real estate agent with Compass in Denver.

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“I hear this almost every day with brokers: ‘Oh, I showed my new listing to the most adorable couple yesterday. They are fit for this house. I love them,’” Mr. James said. “Now, if an offer comes in from them that’s very close to another buyer’s offer, guess who’s going to have the advantage in that situation?”

Mr. James recommends that buyers make a good impression right off the bat.

“It starts the minute you walk through the threshold,” he said. “You need that agent to recognize you and recognize that you’re going to be as accommodating as possible.”

He warns that buyers often make the error of trying to play hardball too soon.

“There are some buyers who go into a property they really like, but they feel they have to put it down because they think that’s the way of getting a lower price,” Mr. James said. “Well, that never works.”

Instead, he suggests this: Ask nice questions. Never make demands. Buyers who may have concerns about the property can have their agent handle that later on with the listing agent. 

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“You need that agent to want to sell you to their seller,” Mr. James said.

Ms. Abbey suggests asking the listing agent what terms of an offer are the most important to the seller: Does the family want to stay in the house for 60 days following closing? Is it more important that they close as quickly as possible? A buyer and their agent can then structure their offer accordingly.

Personalizing an offer needn’t stop there. Ms. Abbey has even gone so far as to look up the sellers on Facebook and tailor her offer letter based on their profile. In one instance, she found that the sellers had a family dog that looked similar to her client’s. In their offer, the buyers attached a family photo with the dog included. In another instance, she learned from the seller’s agent that they were fans of theater, so she included tickets to a show at the Denver Center for the Performing Arts to sweeten the deal.

“A buyer can’t come on too strong,” she said. “Sellers want more, more, more.”

A Gushing Love Letter May Do More Harm Than Good

In the past, Ms. Abbey encouraged buyers to write “love letters” to sellers, detailing why they loved the house. But last year, the National Association of Realtors advised that real estate agents back off the practice. Link for this? They warned that love letters—beyond just gushing about a home—could also reveal a buyers’ sexual orientation, religion, or race, thus making sellers and their agents vulnerable to discrimination accusations under the Fair Housing Act, which prevents people involved in leasing and selling homes from discriminating against people based on their race, sex, religion, disability status, national origin or family status.

Ms. Abbey has since stopped the letter-writing. Other agents agree that the letters probably aren’t worth the risk they pose. 

“You have to be really careful about what you say in those letters,” said Judy Zeder, a sales associate with the Jills Zeder Group in Miami. “So many sellers are getting letters, and they’re beginning to sound very similar.” 

The practice has become so common that many sellers say they don’t even look at the letters anymore.

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Choosing an Agent With a Strong Network

Ultimately, the relationship that’s the most important is not the one between buyer and seller, says Ms. Zeder, but rather the one between the buyer’s and seller’s agents.

“When the agents know each other, they may know from having worked with them for a long time that they work hard to make a deal happen,” Ms. Zeder said.

Reputation matters. Ms. Abbey admits she has a “list” of agents she doesn’t like to work with because they are difficult to work with, or may try to negotiate last-minute price changes or contingencies. A buyer working with an agent like that may be at an automatic disadvantage, she said.

Reputations work in the opposite sense, too.

“I’ll have a listing agent say to me, ‘I trust you. I know you’re going to get to closing. I know you know how to solve problems,’” Ms. Abbey said. That makes her client more likely to get chosen among a pool of good offers.

Nothing Beats a Firm Offer

Most agents will agree on one thing: All the personal touches in the world don’t matter if the offer isn’t strong.

“The cleaner you can make your offer, the better the chance that you’re going to get the property,” Ms. Zeder said. Lining up financing ahead of time, making a cash offer, or putting up earnest money are ways to get an offer noticed right away.

If a buyer’s offer is at first passed over, agents still encourage making a backup offer.

Buyers drop out for all kinds of reasons, Ms. Zeder said. They might identify a problem with the house during an inspection, the appraisal doesn’t work out, or they get buyer’s remorse. A strong backup offer can also make the seller less willing to cooperate with the first offer

“Usually, if the first buyer tries to renegotiate or reshuffle the property, the chances are you’re going to get the offer,” Ms. Zeder said.

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Beyond the numbers game, showing some enthusiasm doesn’t hurt. Ms. Abbey knows from experience that buyers who are more excited about a property tend to be more accommodating during the appraisal and inspection, rarely trying to renegotiate at the end. Ultimately, that may end up benefiting a seller.

“Sellers want to make sure they pick right from the beginning because that’s how they make the most money,” Ms. Abbey said.

Mr. James said that some sellers will take the time to work with a buyer they feel is right for the property.

“The seller could then say to the agent: ‘Go back to that couple’s agent and see what the story is with them. They look like they can really afford this and they seem so right for this house—let’s see if we can get them up,’” he said.

“They lived there, maybe raised their family there,” Mr. James added. “It’s important to them on some level, who they sell their home to.”