But what worried her most was that the baby might bang her head on the way to the emergency room, causing her to bleed uncontrollably inside her skull. “I was so nervous I went down to the basement and got a bike helmet,” Dr. Costello said.

It turned out that the child had a disorder called I.T.P., for idiopathic thrombocytopenic purpura, which can develop after a routine viral illness. The immune system, revved up to fight the virus, somehow begins to attack the body’s own platelets.

Fortunately, the baby made a full recovery. The disorder usually resolves on its own, with drug treatments available for children whose platelet counts dip dangerously low.

When the occasional nosebleed becomes frequent and uncontrolled, or the routine bumps of an active toddler turn into constant bruising, it is frightening for parents and often challenging for doctors to diagnose. Successful hemostasis — the stopping of bleeding after a blood vessel is broken or torn — is an incredibly complex process.

Consider von Willebrand disease, an inherited disorder that — like the better-known hemophilia — is caused by a deficiency in one of the essential factors that govern the blood’s ability to clot. (The two disorders are caused by different deficiencies.) Screening tests have suggested that as much as 1 percent of the population may have the abnormally low levels, or abnormal function, of von Willebrand factor that cause the disease, although many never have bleeding problems. Children with this condition often have severe nosebleeds that will not stop, and they can bleed dangerously after a routine tonsillectomy.

Von Willebrand disease is most commonly treated — if it needs to be treated at all — with a drug called desmopressin, which can be used when a child needs surgery, or at the beginning of a menstrual period.

Abnormally heavy menstrual flow, or menorrhagia, is another common problem for girls and women with von Willebrand disease — which, unlike hemophilia, is not a sex-linked trait.

Most types of hemophilia are inherited on the X chromosome and therefore show up only in males, who have no second, normally functioning X chromosome. Queen Victoria, herself unaffected, was a carrier — thus that famous pedigree by which royal children with hemophilia married into so many ruling families of Europe.

Von Willebrand disease, in contrast, is inherited on a nonsex chromosome, and it shows up in males and females. The National Hemophilia Foundation is running an awareness campaign aimed at women who may have von Willebrand disease without knowing it.

Hemophilia, too, can show up unannounced. Dr. Catherine Manno, a hematologist who is the head of pediatrics at New York University, points out that almost a third of cases occur in children without a known family history of it.

“They usually present after the first birthday,” she told me. “Even with no clotting factor, children with hemophilia can have completely normal births, and if they’re not circumcised, they can have little to suggest they have a bleeding disorder.”

It’s when they become more active, as they learn to walk, that they begin to have the bumps and bruises that signal something is amiss.

Hemophilia is treated with replacement therapy; the missing clotting factor is provided as a concentrate injected or infused into the blood.

Many parents, seeing increased bruising, think first of leukemia. Dr. James B. Bussel, an expert on I.T.P. who is a professor of pediatrics at Weill Cornell Medical School, told me that part of his job was to reassure those parents that leukemia can be ruled out if the red and white cell counts look normal and if the child does not have enlarged lymph nodes or an abnormal liver and spleen.

“If they present with bleeding and/or bruising and they get checked by the pediatrician, and the platelet count is very low, then if the other counts are normal and there’s no major finding other than signs of bleeding on exam, then they almost certainly have I.T.P., especially if the bleeding developed recently,” he said.

There’s another concern that often comes to mind for doctors — or teachers, or neighbors — when a child has abnormal bruising. “The public has been educated to report this sort of thing,” said Dr. Manno, of N.Y.U. It’s important not to miss abuse, but it can be hard to endure that recurrent suspicion.

“If you’re living with the burden of a chronic disease in your beloved child,” she went on, “and someone approaches you and says, ‘How did your kid get those bruises?’ that’s very offensive to people.”

Some bruising is to be expected in active children. The most common sites are the outer side of the arm and the front of the leg; bruises that show up elsewhere are more worrisome, and bruises that show up where there has been no bang or bump are most worrisome of all. Pediatric hematologists describe parents who report that their children develop bruises where they’re touched or picked up, and those children definitely need to be evaluated.

“In this day and age when doctors have to turn around four to six patients in an hour, trying to take a careful history is not easy to do sometimes,” said Dr. Robert R. Montgomery, a pediatric hematologist and von Willebrand expert at the Blood Research Institute in Milwaukee.

And sometimes, he continued, “bruising will be dismissed — oh, all children have bruises — but it’s important.”