gl lighting - specular shininess

After doing a little research, thinking, and playing around, I discovered that the reason I couldn't get that nice white glossy shininess on my object is because it's textured (which means that pure white is only as pure as the texture is). So the question is, how do I use lighting to cause the texture to become more white that it's suppose to be? I tried to use blending to draw 2 objects, one is the object, and the other is a white untextured version that's transparent. But this does funny things with the depth buffer, and it's hard on the CPU/GPU when you want to draw a good number of these objects. How would I accomplish this?