But about once a month, an ambitious parent with cash to burn asks Desrosiers, a pediatric endrocrinologist in Florida, if he would be willing to give growth hormones to a short but otherwise healthy child.
Desrosiers turns these patients away, but he says the requests still come.
Just last week, the father of a young baseball player -- a 14-year-old who was already 5 feet 6 inches tall -- expected Desrosiers to prescribe recombinant growth hormone (rGH) to add height to his budding athlete.
"He wanted to make his kid big, and he thinks he's going to walk out with the shots," said Desrosiers, director of pediatric endocrinology at Arnold Palmer Children's Hospital in Orlando. "He was willing to pay more than $45,000 a year, and didn't even bat an eyelash."
Desrosiers said he even gets requests for growth hormone from "Jolly Green Giant" families, where children are likely to be tall.
In 2003, the U.S. Food and Drug Administration approved the use of rGH for children with idiopathic -- or unexplained -- short stature, without a diagnosed metabolic hormone deficiency.
These synthetic hormones have been a boon for children who are at the bottom of the growth curve, whose predicted heights would never exceed 5 feet 3 inches for boys and 4 feet 11 inches for girls.
But with a society that is more comfortable with medicating children, the demand has opened a Pandora's box for parents of so-called "designer children" who view being short as a stumbling block to success in life.
These treatments come at a cost -- some estimate $35,000 an inch -- and when used in higher doses can shorten life-span by predisposing children to diabetes, scoliosis and cancer, according to some studies.
"We are actually making kids who are now considered healthy sick," said Susan Cohen, co-author of the new book, "Normal at Any Cost."
"The treatment of height turns out to be a cautionary tale," she told ABCNews.com. "You have to assume that parents want to do the best for their kids, but the best of parental love and the desire of a doctor to fix things is a huge industry."
According to Dr. Wilma C. Rossi, clinical associate professor for pediatrics at Children's Hospital in Philadelphia, the number of parents seeking growth hormones for their short, but healthy, children is on the rise.
"Overall, tall is considered 'better' than short," Rossi told ABCNews.com. "Children are perceived to be at a disadvantage socially and athletically if they are short. Parents often worry about the child's emotional health since they are sometimes teased for being shorter and looking younger than their peers."
The average American adult male is 5 feet 9 1/2 inches tall and the average woman is 5 feet 4 inches tall, according to the Centers for Disease Control and Prevention.
Height is largely determined by genetics, and hormones secreted by the pituitary gland -- a pea-size organ in the brain -- are responsible for growth.
Most research shows that while it's tough being short in grade school, the outcomes of shorter children are no different than their taller peers in adulthood.
"It seems contradictory, but growing up short in and of itself doesn't cause development issues," said Ellen Frankl, author of the 2006 memoir, "Beyond Measure."
"They are fine," she said. "It's the prejudice and stereotypes from other peers, teachers and principals."
Many experts worry that there are no long-term studies on the health effects of growth hormone on healthy children. And medical ethicists point out that treatments are most effective when a child is too young for informed consent.
Shots, usually given six times a week, are expensive -- up to $4,000 a month -- and must be given before puberty when bone plates close. And in most cases, height gains are minimal.
"If our kid has a life-threatening illness, we want to go to the doctor, but if the kid is healthy, how much risk do we want to take for only one or two inches of height?" asked Cohen.
Human growth hormones have a dark history.
From 1963 to 1985, about 27,000 children worldwide were injected with human growth hormone (hGH) obtained from the pituitary glands of cadavers. Some contracted the deadly Creutzfeldt-Jakob or Mad Cow disease. In all, 26 out of 7,000 Americans -- and many more in Europe -- died, according to statistics from The National Institutes of Health.
But after 1985, with genetic engineering technologies, rGH and IGF-1, an insulin-like growth factor, were developed to treat children with hormone deficiencies.
In 2003, Eli Lilly and Company requested approval to market its rGH, with the brand name Humatrope, to those whose height put them roughly in the shortest 1.2 percent of the population.
"This is not cosmetic use," Dr. David Orloff, the agency's chief of endocrinology, told The New York Times at the time.
Today, Lilly spokeswoman Teresa Shewman told ABCNews.com that it "does not condone any use outside of its approved indications" and defended Humatrope's safety record.
But a 2006 article in Pediatrics magazine by David B. Allen -- "Growth Hormone Therapy for Short Stature: Is the Benefit Worth the Burden" -- warned about long-term risks.
These therapies are so successful, that doctors are using higher dosages to achieve maximum height, according to Allen.
"The transmission of Creutzfeldt-Jakob disease via pituitary growth hormone is a poignant reminder to take a farsighted view of the potential ramifications of long-term hormonal therapy," he wrote.
As for parents who want to beef up their children, "We chase those people out of our offices," said Desrosiers. "There are not many places in the country where they have fallen into the unethical trap."
But some report that their pediatricians are too eager to recommend growth hormones.
Atlanta, Ga., mother Ronica Brown said she was pressured by a doctor to consider rGH because of her son's short stature, even though no deficiency had been found.
"It is rather disconcerting that physicians are recommending interventions that for all practical purposes are unnecessary, and may, in fact, create clinical problems for otherwise healthy patients," Brown told ABCNews.com.
"It is like saying there is nothing wrong with brown eyes, but although this drug is approved for treatment of cataracts, it also lightens the color of the iris so we are recommending it for you."
But parents of children with legitimate growth hormone deficiency say the new demand for rGH has compromised their access to good diagnosis and treatment.
Insurance companies now make it harder to seek reimbursement for rGH. Doctors are also more suspicious of parent requests for testing.
At the age of two, Calli Chambers was the size of a 9-month-old and had only five teeth. The soft spot on her head, which normally closes in infancy, was still open.
"No pediatrician caught that," said her mother, Jennifer Chambers of Severn, Md. "They said you are not that tall, and she's been sick."
An endocrinologist later prescribed rGH and now, at 4, Calli has hit the 10th percentile, growing 7 and 3/4 inches and gaining 10 pounds. Treatment also helps her "kidney reflux," a disorder associated with the lack of hormone.
"I think it's hard enough to get approval when the kids need it," said Chambers, who now works as a consultant for the Magic Foundation, which advocates for those with pituitary disorders.
Melissa J. Grey, of San Diego, Calif., said the lives of her two sons, both diagnosed with growth hormone deficiency, have been "transformed" by rGH.
Her 11-year-old jumped from the second to the 48th percentile in two years.
"He now sleeps well, has a normal appetite, has muscle tone for the first time and enjoys a host of other health and metabolic benefits, such as cardiovascular strength and improved aerobic capacity," she said.
"For every child whose parents simply want them taller, there are dozens who legitimately need treatment and are unable to afford it," said Grey, 44. "I fought for over five years, seeing a plethora of pediatricians and pediatric endocrinologists before someone legitimized my concerns and ordered the appropriate and lengthy testing for my children. It was this 'designer child' bias, along with the fact that I am short, that cost my kids much of their childhood."
"There is a tremendous misconception that this is a steroid and that my children are artificially doping, when in fact they have a legitimate congenital condition." she said. "But I want my kids to be proud of who they are. They are so much more than their genetics."
She said her children are "blessed to live at a time when science has made true health safe and possible."
But other parents, like Chairiah Myntti of St.Augustine, Fla., worry about the dangers of growth hormone therapy.
Myntti, now 38, missed a bullet when her doctor urged her mother to consider giving her hGH in 1984. At 13, she only weighed 73 pounds and was 57 inches tall.
"My mother declined the hormone growth and said 'I'm just going to let nature take its course," Myntti told ABCNews.com. "She told me she was afraid the drugs might do something bad to me and make me deformed."
Today Myntti is only 5 feet tall, in part because of her Asian heritage. Two of her four children were also targeted by doctors for their size. Her 11-year-old was so stunted as a baby that Myntti was falsely investigated for child abuse.
Her 16-year-old has been teased for being smaller than the shortest girl in his class.
"If they were to use a growth chart from, say, Southeast Asia, my children and I would be somewhere between average to enormous," Myntti said.
Some children will always be at "the end of the line," according to Dr. Chris Feudtner, director of the department of medical ethics at Children's Hospital in Philadelphia. "A certain portion will always be deemed short. It's unavoidable."
He concedes short children sometimes face bullying, but parents cannot always protect their kids from bad experiences.
"We are trying to create perfect childhood by doing things that ultimately don't empower us to be strong adults," Feudtner told ABCNews.com. "Medicalizing the situation might not give the results we are looking for, even with the best of intentions."