You're in luck! While your cellphone bill itemization will always show all the incoming and outgoing calls (though it doesn't log incoming calls you don't answer) that's a lot harder to peruse than the data that's directly on your iPhone. You cannot set it up so that the calls aren't logged at all, but it's pretty easy to remove a specific call or two, or to clear the entire list.

Further, recent calls is split into two categories anyway, "All" and "Missed". The latter is helpful if you leave your phone in the car and want to see what calls came in while you were offline, for example.

I actually find the "Recents" list quite helpful, particularly since it's so easy to turn a number into a Contact in your address book (I rarely have more than one call from an unidentified number for just that reason) but you're interested in trimming the list, so let's have a look at that.

First things first. In the Phone app, here's what my "Recents" list looked like:

You can see that it no only lists all the incoming and outgoing calls, but it also specifies a geographic area if it's an unknown number (see the first and last entries) and indicates which of the phone numbers was used (based on what you have recorded) for someone that's in your Contacts list.

Let's say that I want to delete the third number on the list, the call from 1 (949) 837-4500. There are actually two ways to delete a number. The lazy way is to simply swipe side-to-side over the number. I do this and a Delete button appears:

If I tap on "Delete" that entry is instantly and irretrievably removed from the recents list, as you can see if you compare the following capture with the first I showed:

If you want to delete a bunch of numbers from the list, however, tap on "Edit" on the top right and every number will now have a small red delete button adjacent:

Tap on the delete circle and the big red button appears:

As you can see, it's easy to delete specific numbers with this approach.

Want to delete everything, however? When you're in Edit, notice the "Done" button on the right, but also notice that there's a "Clear" button on the top left too. Tap on it and...

That makes it easy, doesn't it? So get to the Recents list, tap on "Edit" then "Clear" and you've just removed every entry in your call log, whether it was one you originated, one you answered or one you missed.

Hope that helps you cover your tracks!