Speaking too quickly and saying "um" a lot can make you sound really nervous. I'm not the best at sounding confident... especially on the phone, my voice gets a lot higher pitched, and I do talk faster than normal... when I tried to correct this, I just couldn't seem to because, well, I get nervous on the phone! I also talk this way to people I've just met, and strangers in stores. I'm not working now, but when I was, I loved working with customers but I knew I still sounded really un-confident most of the time...
Honestly, I haven't gotten any better at making my voice sound confident, so I can't help with that part. (TRICKED YOU HAHAHA)
But I've found a way for it to stop being a problem for me! I've noticed that people tend to like someone who seems confident, OR someone who seems up-front and honest. Mixing it with a bit of your own sense of humour can't hurt too much... when I realised it was too hard for me to sound confident and self-assured, I decided I could still BE confident and self-assured, but show it in a different way. In my case, this amounted to having a sense of humour about myself and being the first one to bring something up -- for instance, if I answered the phone to talk to a customer, I would usually mess up several words in a row, go back to fix them and mess up again, and finally get it right. Instead of letting myself feel anxious, I'd bring the mistake up in a funny way say stuff like "Oh gosh, lemme try that again with real words this time!" I don't really plan things to say, I just don't try to hide mistakes I make because I've realised that I'm not the only person that does that kind of stuff.
Anyway, customers always really liked me so it obviously worked~
Might not be your style, but it's something to try if you don't feel like acting your way through talking with customers. :]