Which word means to make English?

The "coolness" argument is the one people always give, but I find it hard to agree with. Most English words used in German (outside of youth culture) seem to be everyday words, not slang. What I do notice is that the English words are almost always a lot shorter than their German equivalents. If people can say Cop in one syllable instead of Polizist in three, or Fair Play instead of anständiges Verhalten, and be understood, they will. (In the same way, the word Rechner is still around — because it's a syllable shorter than Computer.)
Even within English, we've shrunk "telephone" to "phone", "facsimile" to "fax" and "omnibus" to "bus". So maybe German needs to do more of this. O-Ton and E-Gitarre were a start, and even Handy was shortened from Handgerät — but this worked because full-sized German words existed to start with.
By the way, all these loan words are a real stumbling block to foreigners learning German. They have to know what each English word means and how it's pronounced locally before they can use it.