A couple weeks ago, I started an experiment:

    Everything I need to survive in a bag (including a towel, of course).
    My phone lives in the bag, not in my pocket. I take it out of the bag when I want to use it, and put it back when I'm done.
    The bag also contains my tablet, a sketchbook, couple of books, and some other odds and ends (and of course, the towel).
    End goal is to keep the phone on the same level as everything else: a tool, which I use for specific jobs, and then put back in its place when I'm done.

The idea was, I'd try it out for at least two weeks, even if I hated it, in order to get some better data than just trying it out for a few days.
However, after just two days, I decided it was no longer an experiment. I would never go back.
I used a backpack for the bag, and that extra step of having to dig around the backpack to find the phone (I drop it in, and it disappears, just like it should) provides insulation from the immediacy the phone used to represent in my life.
I had often surmised the availability that a cell phone offered was radical, i.e., not natural. It made me a slave to others. Everyone I typically interact with expects calls and text to be returned within the hour, because that's what they would do.
But just having the phone not in my pocket, evaporated any compulsion I had to answer right away. The anxiety of being "available," melted away.
And then there was the other aspect of having a tiny computer at my beck and call. That itch to look things up, scroll through media, revel in distraction.
But again, just that little bit of removal from immediate proximity, of having to dig the phone out of the backpack, helped immensely to curb that obsession.
It made the phone a tool. When I need it for something I fish it out and use it for that task, then it goes away. Same as the sketchbook, the tablet, and the various other things I keep in the bag.
So overall, a successful experiment. I doubt it'll be the same silver bullet for everyone, but I'm really thankful it helped me find some balance and peace in my digital life.
One final note though: to stop me from reflexively putting the phone in my pocket, especially at first, I figured I should have something else take its place. I decided on two things: my pocket watch, and my pocket knife. I had carried both these things during high school, but got my first cell phone shortly after graduation. I ended up ditching the watch, since the phone told time, as well as ditching the knife, since I didn't want to scratch up the phone.
Having these two tools back has been amazing. With the pocket watch back, I ditched the wristwatch, which always felt like it literally shackled me to a clock. And the pocket knife comes in handy way more than I expected.
In closing: we should have never taken the phone off the wall.