In most dynamically typed languages, variables are created without declaring their type. This way of programming allows variable reuse, so that variables sometimes hold different dynamic types in the same scope. Besides, it is also common to use the same variable to hold different dynamic types, depending on the execution flow of the program. When dynamically typed code is compiled into Java and .Net, the dynamic variables are usually generated as Object references. The approach of declaring variables with the top type (e.g. Object in Java and .Net) requires unsafe and inefficient type casts and, sometimes, the use of reflection. We propose the use of SSA (Static Single Assignment) transformations to facilitate inferring the type of dynamically typed local variables. The approach has been included in an existing compiler for the .Net framework. The result is that dynamically typed code performs significantly better when the SSA transformations are used, and it outperforms C#. Our technique reduces memory consumption at runtime by 35%, but increases compilation time by 13%.