Each year, in the rarefied world of private-school admissions, there is a new batch of horror stories. But this summer, one tale, more than any other, made its way around the gossip circuit.

A well-connected set of parents (both grew up in the city) with a young child applied for a kindergarten spot to the same prestigious Upper East Side school in which their older child was happily ensconced. They were told by the head of the celebrated school that to be safe — given the “no-sibling” policy at their older child’s school — they should apply to several schools. The parents did.

But their younger child was as bright and engaging as the first. They assumed that private schools adopt no-sibling policies to ensure that less capable younger siblings aren’t granted admission. And, let me not forget — they weren’t new to this school. One of the parents had attended the school for more than a decade, and the family had supported it financially in grand fashion.

When their child was rejected, they were stunned — but not too stunned to send in the deposit check to the equally prestigious private school across the park that welcomed their child with open arms.

“I am so mad,” the mother told me. “All I want to do is pull my older kid out of that school, but he’s happy. As much as I dream about it, I just can’t. At least the schools have the same calendar, but still — two different fund-raisers, two different conference days, two different drop-offs and pick-ups. We both work. It’s absurd.”

We all know the deal: More families are staying in the city, and when it comes to the number of children, three is the new two. All of this is happening while the number of kindergarten spots has remained roughly the same.

And we also know the ugly truth: that whatever these schools say, there are some children who are just going to be accepted. If a board member is your closest friend, you’re in good shape. If you’re related to a large donor or to a long-time teacher or the head of school — you’re in good shape. But if you’re a fairly well-off parent of two or three lovely, smart children — watch out. You never know how many ethnicities need to be represented in each class, or how much financial diversity the school is trying to create. You also don’t know how many board members are writing letters for children who are applying for your child’s very class.

“The no-sibling policy was originally meant to help parents recognize that not all children belong at the same school,” an admissions director (of a school that “doesn’t guarantee siblings but tries to accommodate them”) said. “And of course, this is true. Some children are more self-motivated than others. Some need nurturing. Some thrive with structure. But that’s not really what’s going on anymore.

“The no-sibling policy — and the elimination of alumni preference — are two more ways for schools to deal with the fact that they have far more applications than spots,” she added. “When your perfectly bright and adorable younger child is rejected — because ostensibly they’re not a good fit for the school, or they need another year to mature, but you know otherwise — what’s really going on is that for a variety of reasons, the school needs to take other children more than yours,” she said.

When I first heard this story, I felt enormously grateful that my children attend a school that accepts siblings automatically, and that’s not just because I have a lot of children.

Having entire families attend a single school creates community and school pride. Younger children are comforted by seeing siblings in the hallways, and older children get a kick out of having siblings cheer them on at sports matches. It’s great when your older child’s best friend has a sibling in the same grade as your younger child. There’s a certain familiarity and warmth when a family has the same teacher for the second time. And you are less likely to fret over your child’s weaker areas if you know that the school is your partner in helping you provide your child with the resources he needs — as opposed to one step away from suggesting that your child isn’t a good fit for the school.

Did it ever occur to educators that one sign of a school’s success is its ability to accommodate a wide range of capabilities? Some children excel at math and have deficits in language. Some linguists will never understand derivatives in calculus. One of my favorite features of my children’s school is that in their classes, there are gifted students as well as those who are far less capable. The school is equipped to handle a range of abilities. There is not just one kind of child who can flourish at the school.

Private schools should stop pretending that a no-sibling policy is meant to protect less academic younger siblings whose fragile sense of self will be shattered at their older sibling’s school. In some cases this might be a risk. But in far more instances, it’s just another excuse given to otherwise deserving families, who suffer at the hands of other families who will create too much controversy if their children are rejected.

sarasberman@aol.com