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This article develops a flexible binomial model with a “tilt” parameter that alters the shape and span of the binomial tree. A positive tilt parameter shifts the tree upward while a negative tilt parameter does exactly the opposite. This simple extension of the standard binomial model is shown to converge with any value of the tilt parameter. More importantly, the binomial tree can be recalibrated through the tilt parameter in order to position nodes relative to the strike price or barrier of an option. The rate of convergence is improved as a result. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 817–843, 1999