Internet commentators have been nosing into whether Mr. Trump habitually snorts Adderall, a stimulant medication prescribed for Attention Deficit Hyperactivity Disorder (ADHD). Derisive and joking commentary pervades this buzz. However, if true, we should probably applaud the allegations. First, they constitute at least tacit acknowledgement of Mr. Trump’s ADHD. Secondly, they indicate his acting in ways that might actually mitigate some of his ADHD-driven problems.

Several lines of cocaine, I mean investigation, lead to Mr. Trump’s purported history with stimulants. Reports going back decades assert that doctors prescribed Mr. Trump phentermine. The FDA approved the stimulant medication phentermine for weight-control, but physicians also prescribe it off-label to treat ADHD. Phentermine prescriptions receive less government scrutiny than more tightly controlled stimulants like Ritalin or Adderall. During the presidential campaign two years ago, pundits extensively discussed Mr. Trump’s sniffing, grimacing and hyperactivity, and whether these behaviors indicated a habit of snorting cocaine or other stimulants. Months ago, individuals who worked on the reality show The Apprentice claimed that Mr. Trump routinely snorted Adderall while on the set. The issue achieved greater prominence following Mr. Trump’s recent Presidential Address, with a flurry on Twitter noting that his frequent sniffing and visibly dilated pupils might both indicate ongoing Adderall snorting.

I examined video footage of the border wall Presidential Address, comparing it to his other presidential performances. Mr. Trump’s pupils are substantially larger during the Address than during other speeches, under what appear to be similar indoor lighting conditions. (Brightness strongly influences pupillary dilation.) However, even more blatant than a change in the size of his pupils, during the Address he made many fewer head and body movements, many fewer hand gestures, twitched less, and uttered more organized sentences, in a calmer cadence, than he displays elsewhere. While some of this behavior may be in direct response to the structure of reading from a tele-prompter, we have certainly seen him go off track in other speeches, despite help from a tele-prompter. The combination of simultaneous physiologic, behavioral, and cognitive changes in the president’s behavior strongly suggest that during the Address he used stimulant medications in order to behave more coherently.

Those deriding the president’s reputed drug use attribute many of Mr. Trump’s mannerisms to his alleged snorting of stimulants. In this framing, his non-sequiturs, verbal inconsistencies, sniffing, twitching and restlessness are all symptoms of habitually abusing stimulants. Indeed these can be common behavioral responses to stimulant medication. However, a more accurate assessment of the situation would address the evidence that we are examining the putative effects of stimulants not on a “normal” individual but on a man with severe ADHD.

The following constitute an outline of the compelling case for Mr. Trump’s ADHD: He displayed symptoms of ADHD in childhood. Observable behaviors recorded on video suffice for fulfilling the current formal definition of ADHD; we do not need knowledge of his emotional state, motivations, or internal thoughts to diagnose this condition. He pervasively continues to display a broad array of ADHD symptoms. No other disorder comprehensively explains all of these behaviors. The presence of ADHD does not indicate the absence of other mental health problem; actually other mental health issues commonly co-occur with ADHD. He displays many aberrant behaviors unattributable to ADHD. Furthermore, other people with ADHD only resemble Mr. Trump in their shared ADHD traits, we should not stigmatize them with Mr. Trump’s particularly virulent lie-about-the-border, abuse-a-reporter, Adderall-snorter, generalized-disorder form of ADHD.

The myth persists that ADHD brains are “wired backwards” so that stimulants, which rev up most people, directly calm down individuals with ADHD. Unpacking this myth begins with understanding that people with ADHD are not unable to focus, rather their control of attention is impaired. Hence they tend to be overly distracted in some situations, (jumping off topic, like suddenly commenting about Rosie O’Donnell during a policy statement) and overly focused in others (remaining hyper-focused on a topic long after others have moved on, like harping about Hillary’s e-mails). Most people with ADHD have a myriad of thoughts ping-ponging around in their head at any instant, with a proper dose of stimulant medication they can focus on one item at a time and consider it at more depth and leisure. The frenetic behavior, the bouncing back and forth, the impulsivity, the self contradictions of ADHD are all a result of being unable to control attention, and when someone gains control of their attention, they can process their environment and their own thoughts in a more organized, calm manner.

All of us require the appropriate amount of stimulation to perform optimally. With too little stimulation we are bored, unengaged and underperform, and with too much we become too agitated and derail our work. Medications like Adderall, Ritalin, or phentermine help individuals with ADHD prolong their stay in that optimal range of stimulation. Although people with ADHD can be pushed into over-stimulation with too much medication, this usually requires a much bigger dose than what elicits over-stimulation in individuals without ADHD.

The baseline, unmedicated, unfocused behavior of ADHD — the rapid, disjointed speech, jumping from topic to topic, the physical restlessness — the manifestations of under-stimulation — do resemble, and are often confused with over-arousal. Even professionals frequently assess this incorrectly. Over many years of working with adults with ADHD, I have heard dozens of reports describing pharmacists who balked at filling orders for Ritalin or Adderall and who even told patients that their behavior looked like they were already over-stimulated. Even worse, I have had patients with severe ADHD who were hospitalized in the midst of crises, and the doctors forbid the continuation of stimulants on the in-patient ward, out of the mistaken fear that these already frenetic-appearing patients would become more riled up. In the instances where I was able to convince the doctors and nurses to allow the patients to resume their stimulant medications, the patients calmed down, became able to listen to, process and follow directions, and the staff were amazed and relieved.

Hundreds of studies and millions of patients support that the stimulant medications very frequently succeed in reducing ADHD symptoms. More than two dozen studies indicate that patients taking stimulants end up with brains that appear more normal than those of untreated individuals with ADHD — which is in direct contradiction to the fear that these drugs “rot brains”. However, stimulants are not perfect medications. Prescribed stimulants can cause horrible problems like addiction and psychosis, and snorting the medications increases these risks. I rely extensively on non-medication approaches and non-stimulant medications for treating ADHD. I also prescribe stimulant medications, which have helped a few hundred adults minimize their ADHD impairments and have harmed fewer than a handful; these rates correspond with the published risks.

I hope to have converted snorts of derision about Mr. Trump’s purported stimulant use to snorts of enlightenment. Stimulant medications help many adults with ADHD improve their focus on, and engagement with, their worlds. Those who seem most “over-stimulated” to begin with (but are actually under-stimulated) are often the patients who respond most powerfully to ADHD medications. It is not surprising that people have a hard time wrapping their head around medications that produce hyperactivity, rapid and disjointed speech and impulsive behavior in some people and alleviate it in others. Yet Mr. Trump, his immediate circle, and the whole country will benefit from effective treatment for his ADHD. Rather than riffing on his sniffing, maybe we should be supporting his snorting.