Trying to eliminate the Binkie!

We've been slowly trying to eliminate/reduce the use of the Binkie...affectionately called "Mine" in our house!  She's become quite attached and uses it as a comfort item. As a child thumb-sucker, I'm hoping this will be easier than I remember quitting my habit.  It's now been 36 hours+ of not having our Mine!!!  She's only asked for it a few times, but...apparently unable to find it (hehehe...hidden well!). HOWEVER...NO NAP TODAY!!!!  Is this our punishment?!?!  We'll see how this goes.  Wish us luck.  And wish us well with baby boy...because he'll most likely have a Binkie at times.  I'm hoping we'll be able to break the habit sooner than we did with Kayleigh!