Preventing light spill from an umbrella

Question

I've been reading Strobist lately and love the moody half-lit-half-dark effect in a lot of these types of photos. I'm a beginner and have a limited equipment budget, so I got a 45" reflective/shoot-through umbrella.

It gives great softness for the really low price. However, I find that I can't get the really dark areas/high contrast in my portraits. I think that this is because the excess light from my strobe is bouncing off my room walls and coming back at my subject. This effectively creates a new "ambient" light source (I've killed the real ambient) that prevents the deep shadows.

What are some good ways to work around this? Bonus points for being low-cost.

Answer

Another option is called "bookends"; 4x8 sheets of foam board, hinged together with tape. Leave one side white and use it as a reflector, paint the other side black and use it to eat light.

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