Karlie Kloss and Joshua Kushner are officially on their honeymoon, and it's definitely an adventure. The newlyweds, who tied the knot in front of 80 people (sans Taylor Swift) in upstate New York on October 18, are currently on safari in South Africa, where they've been documenting it all on social media.

So far, they've hung out with elephants—while soaking in an infinity pool—seen at least one lion, and traveled around in an open-air vehicle. Kloss has also dressed up for the occasion, in a straw hat and floral print outfit, as Kushner shared a photo of her taking in a panoramic view. Not surprisingly, her outfits have been a lot more casual than the custom Dior gown she wore to the wedding.

While the trip marks their honeymoon, it isn't the first one they've taken since marrying—right after their ceremony, the couple took a short trip to a tropical beach, the location of which they didn't give away.

Their secrecy around their "mini moon" is in character for Kloss and Kushner, who have kept their relationship largely private throughout—and especially in the wake of Kloss's new brother-in-law Jared Kushner starting his political career with the Trump presidency. Kloss did open up about the awkwardness of that family dynamic recently, though, saying that her values couldn't be more different from those of her brother- and sister-in-law. “At the end of the day, I’ve had to make decisions based on my own moral compass—forget what the public says, forget social media,” she told Vogue. “I’ve chosen to be with the man I love despite the complications. It’s frustrating, to be honest, that the spotlight is always shifted away from my career toward my relationship. I don’t think the same happens in conversations with men.”

Kloss also confirmed that her Kushner is a lot different from the Kushner the public has grown to know. “Josh and I share a lot of the same liberal values that guide our lives and the things we stand for,” she added. “We’ve really grown together personally and professionally. Josh knows that I’m just a nerdy, curious human being. I think that’s why he loves me. We have each other’s back.”