  We develop the notion of independent resolutions for crossed products
attached to totally disconnected dynamical systems. If such a crossed product
admits an independent resolution of finite length, then its K-theory can be
computed (at least in principle) by analysing the corresponding six-term exact
sequences. Building on our previous paper on algebraic independent resolutions,
we give a criterion for the existence of finite length independent resolutions.
Moreover, we illustrate our ideas in various concrete examples.
