Skipping the message in voicemails

In my previous flip cell phone, I just pressed the # key to skip the voice mail message from others & get to the beep so that I could leave a message.

On my iPhone 4S, I have to call up the numeric keypad & then hit the # button there.

That adds 1 additional step.

Is there a shorter / faster way to skip the message & get to the beep?

Further, I find that when I hit the # key on my iPhone 4S, it sometimes asks me for a password (like I was the other person trying to get into his voicemail).

Am I just hitting the # key too early? Or is it something else?