Whether one’s attitudes about marijuana cleave closer to Nancy Reagan or Cheech and Chong, there’s no denying that the drug’s bad reputation is slowly burning off. Consider: Seventeen states have decriminalized pot, 18 now allow its consumption for medical reasons, and two (Colorado and Washington state) have conferred upon their citizens the freedom to toke up for any old reason they please. If the history of free enterprise is any guide, it’s pretty easy to guess where things go from here. Legal pot will become branded pot, and branded pot will be advertised pot.

Or will it? According to the results of a study released today by The Partnership at Drugfree.org, while most Americans seem willing to accept legalized marijuana under specific circumstances, they are nearly united in opposing its marketing. “People are not in love with advertising in general, but with marijuana you get a double whammy,” said Steve Pasierb, the Partnership’s president and CEO. “We asked [our sample group], ‘In what way would you be in favor of marijuana being advertised?’ And the answer was no way.”

He’s not exaggerating. Of the 1,603 American adults surveyed (1,200 of whom were parents of young children), a sizeable 80 percent of them declared that, even if pot is made legal where they live, advertising it should not be. This consensus held up despite generally permissive feelings toward pot. Seventy percent of respondents supported legalizing cannabis for medical purposes, and 43 percent admitted to having smoked it themselves. But when asked to name the place where marijuana advertising would be most appropriate, the No. 1 response was “nowhere.”

Nevertheless, the study’s results also demonstrated that Americans have developed nuanced attitudes about the legalization—which often means commercialization—of pot. Twenty-one percent of Americans were willing to live with marijuana advertising if it's online, and 17 percent were OK with it appearing inside of retail stores. But those numbers fell through the floor when it came to any media likely to be seen by children. A mere 3 percent of respondents were comfortable with the idea of pot being advertised in video games, and 4 percent were willing to countenance the idea of celebrity endorsements. (Sorry, Michael Phelps.) Pasierb explained that parents tend to view marijuana’s marketing as analogous to ads for cigarettes or booze, “and if parents don’t like the advertising for those two things,” he said, “they really don’t like it for this one.”

Not that they’ve seen much of it. Since the federal government still regards ordinary weed as a Schedule I Controlled Substance, and many jurisdictions that permit its possession haven’t ironed out all the sales and regulation issues yet, marijuana marketing is still in its infancy. But with estimates of the value of the legalized marijuana segment projected to hit $47 billion by 2016, observers expect this maturation to happen pretty fast.

Indeed, it’s already begun. California-based Arcview Group, for example, hosts networking events that put cannabis-product manufacturers together with venture capital investors. There’s a National Cannabis Industry Association, too. Deputy director Betty Aldworth believes that “just like any other product, as the marijuana market matures, so will its advertising and branding.” Los Angeles-based marketing consultant Cheryl Shuman has—forgive us—let her entire practice go to pot. “Advertising and branding for the sector is already 100 percent in gear,” Shuman told Adweek. Shuman said several media agencies have contacted her in hopes of reaching out to what she calls “the new breed of cannabis consumer,” which presumably means the legal kind. And, just for a goof, The Daily Beast recently approached two major creative shops (Mother New York and Pentagram) to see what they’d do with a marijuana brief. The amusing results included an advertisement showing a chocolate-chip cookie along with the caption: “Good, it’s working.” (You have to have had the munchies to get that joke.)

All kidding aside, brands currently considering joining the “Green Rush,” as the legalized-cannabis trade is often called, might want to mellow out a while. Earlier this year, former Microsoft executive Jamen Shively pledged to raise $10 million in financing for a chain of Starbucks-style marijuana shops called Diego Pellicer. A joint, says the company’s website, “should be savored, analogous to how one enjoys a fine cigar, a premium chocolate or cognac.” But even weed advocates panicked at this brashness, pointing out that until the DEA decides how to deal with state legalization measures, Shively’s first big location might be the federal pen. Meanwhile, as the Partnership’s study makes clear, brands so open about promoting marijuana use might find something even worse waiting for them: angry parents.

Which raises a final point: Now that marijuana’s historically nefarious image is softening a bit, will the Partnership have to reconsider its own marketing message regarding the risks of using it? Pasierb says no. “Our message is already nuanced about the general risks of marijuana,” he said, adding that his group never equated pot with harder drugs like heroin or methamphetamines. Still, Pasierb added, “One thing we are hearing is parents asking us how they can talk to their kids about marijuana.”

And that, he said, will be a challenge far bigger than most marketers have to deal with.