How many Collatz conjecture elimination patterns are there?

Question

The Collatz conjecture is an amazing thing. For people who don't know, the Collatz conjecture is the conjecture where you take any natural number. If that number is even, divide by two. If it is odd, multiply by three and add one. The conjecture is that this process will always return to one. Looking at it, I know when testing I can skip all even numbers, because when you divide by two, you get a smaller number you already tested. And I can skip every other odd number, because when multiplied by three and is added to one, you will get a multiple of four, so you can divide by two twice, and you will get a number smaller than the original which you have already tested. My question is, can I eliminate any other number patterns? Or is there something I'm missing about the ones I already have?