How do I improve the reflections on the black wine glass render?

I need to improve the reflections on this wine glass. I marked the things that need to change. The reflections look too messy and I need them to stay off the logos. Around the cup bit the reflections don’t cleanly follow to very edge of the glass. I need to be able to put wine in it as well, but that seems to work pretty good. I got the glass working pretty well, I just can’t get the lighting to work right. Can someone do this in the file I uploaded so I can look at and then do it myself? (347 KB)

File-External Data-Automatically Pack into and SAVE file again. This is what you should do in order to allow others to see your image texture. Otherwise we see only pink color where the image suppose to be. So we cannot help you if you dont do that.

Sorry, here you go. Think this did it.

Glass_Reflections.blend (661 KB)