Katy Perry and Russell Brand: NOT On the Rocks!

Russell Brand and Katy Perry have been subjected to headlines about their supposed trouble in paradise recently ... heck, since the day they got married.

But in the wake of the most recent groundswell of speculation - Russell reportedly cavorting with brunettes not named Katy - the couple is fighting back.

"Just cause we don't flaunt our relationship doesn't mean there's something wrong," Katy wrote. "Privacy is our luxury. #tabloidsrtrash #gossipisgross"

Russell echoed his wife's sentiments and cheered her Tweets.

This time around, it was the Daily Mail (UK) and the British weekly magazine Heat that took the lead on spearheading the newest round of reports.

While the Daily Mail reported Brand was seen with a "Katy Perry lookalike," it's Heat that went a step too far, saying they're on "a trial separation."

Citing unnamed sources (obvi), the rag blamed conflicting work schedules and said they've seen each other four days in the past six months.

Perry is far from pleased. Just recently, her legal team hit back at NW, an Australian tabloid, for claiming that she was unfaithful to Brand.

You could be next, Heat.