  We introduce a method for studying monotonicity of the speed of excited
random walks in high dimensions, based on a formula for the speed obtained via
cut-times and Girsanov's transform. While the method gives rise to similar
results as have been or can be obtained via the expansion method of van der
Hofstad and Holmes, it may be more palatable to a general probabilistic
audience. We also revisit the law of large numbers for stationary cookie
environments. In particular, we introduce a new notion of $e_1-$exchangeable
cookie environment and prove the law of large numbers for this case.
