I have a simple white backdrop setup with two off camera flashes setup. One flash is pointed directly at the background to overexpose it to white. The other flash is off camera to the right, shooting through an umbrella to light the subject. The camera was set at f/2, 1/125, ISO 100, at 50mm. The flash behind the subject was at 1/16th power, and the flash to the right of the camera at 1/32nd power.
Image created here: http://www.lightingdiagrams.com/Creator
My issue is that the resulting images have quite a bit of light bleed over the subject(I believe this is the terminology). The way that I would describe this is that the edges of the subject are very soft and blown out. They are not defined well with a nice edge. I would prefer a well defined subject with a pure white background. If I can do this without more equipment that would be preferred.
I got the idea for the flash behind the subject lighting the backdrop from question - How can I inexpensively create the white backdrop look?.
Here is an example of the result that I have right now and would like to improve. I have already done what I could in post production but I know the initial capture can be better and the result better still: