Mapping Smooth Analog Stick Motion Without Having to Press it Down Hard.

Hi all, I have been trying to map my PowerA (xBox 360) controller to respond smoothly to lightly pressing the "Left Analog Joystick" to the left or to the right. I have it working properly, besides a few sensitivity issues. I can only move to the left or right if I press the left joystick down really hard until you hear the button "snap" down into place. However, I want to just lightly press the joystick to the left or right without having to snap the button down into place. Is this possible?

I have been using this website to try and map the controller correctly: http://wiki.unity3d.com/index.php?title=Xbox360Controller

Here are my current Input Manager settings:

My movement code is really simple for trying to get the spaceship to move left and right:

Interestingly enough, I am able to get the smooth motion I am looking for by holding down the "a" or "d" key while lightly pressing the left joystick right or left. Is there a way that Unity can recognize that the move button is being pressed down by the player without having snap the left joystick down into place?