An Arizona state judge is not convinced that a pair of Christian calligraphers should be exempt from serving same-sex couples.

With support from the anti-LGBT Alliance Defending Freedom (ADF), Joanna Duka and Breanna Koski, co-owners of the Brush & Nib calligraphy studio, filed suit in May challenging Phoenix’s ordinance prohibiting discrimination on the basis of sexual orientation in public accommodations. Though they have not yet been asked to provide invitations or other designs for a same-sex wedding, they want to overturn the law so that their eventual refusal to do so won’t be illegal.

On Monday, Judge Karen Mullins rejected the artists’ claim that being required to serve same-sex couples violated their freedoms of speech and religion. She denied them a preliminary injunction as the case proceeds, sending a not-so-subtle hint that their pro-discrimination claims aren’t going to get very far.

ADF had argued that if Brush & Nib is forced to create products that are used in a same-sex wedding, it would constitute compelled speech. Mullins countered that “the only thing compelled by the ordinance is the sale of goods and services to persons regardless of their sexual orientation.” Duka and Koski are perfectly free to publicly state their religious views concerning same-sex marriage and same-sex sexual activity — so long as they don’t publicize an intention to discriminate in their business.

“Plaintiffs confuse conduct with expressive speech,” she wrote. “The ordinance only precludes Plaintiffs from refusing to sell products or provide services to same-sex couples and from stating that same-sex couples are unwelcome as customers.”

Mullins didn’t hesitate to get into the details, explaining exactly why same-sex wedding invitations do not constitute expressive speech, however artistic they might be in design:

Any conceivable endorsement of same-sex marriage that might be conveyed would be conveyed by the act of the marriage itself, and not by the creator or printer of the physical invitation itself. It is absurd to think that the fabricator of a wedding invitation for a same-sex couple has endorsed same-sex marriage merely by creating or printing that invitation. Moreover, there is nothing about the creative process itself, such as a flower or vine or the choice of a particular font or color, that conveys any pledge, endorsement, celebration, or other substantive mandated message by Plaintiffs in regard to same-sex marriage.

Mullins was similarly unimpressed by the argument that designing such wedding invitations would violate the artists’ religious beliefs. They had admitted that they would sell any premade non-custom product to anyone; it was only a conflict if they had to print two male names or two female names. “The printing of names does not hinder in any way Plaintiffs independent exercise of its religious belief by attending the church of their choice, engaging in religious activities or functions, and expressing their beliefs on their business website and literature or in their personal lives,” Mullins wrote. Duka and Koski “failed to assert even an incidental burden on the exercise of their religion.”

Thus, the law doesn’t really burden Brush & Nib, but an injunction blocking its enforcement would significantly burden the city. “The balance of hardships favors Defendant City, given the government’s interest in allowing its citizens to enjoy public accommodations free of discrimination based on sexual orientation.”

ADF isn’t happy with the result and is considering an appeal. Legal counsel Jonathan Scruggs said in a statement, “Artists shouldn’t be threatened with jail time and other penalties simply for making art that is consistent with their beliefs.” The legal organization has filed numerous other suits across the country challenging nondiscrimination protections for LGBT people.