  We outline a general method of constructing finite-range cloaking potentials
which render a given finite-range real or complex potential $v(x)$
unidirectionally reflectionless or invisible at a wavenumber $k_0$ of our
choice. We give explicit analytic expressions for three classes of cloaking
potentials which achieve this goal while preserving some or all of the other
scattering properties of $v(x)$. The cloaking potentials we construct are the
sum of up to three constituent unidirectionally invisible potentials. We also
discuss their application in making $v(x)$ bidirectionally invisible at $k_0$,
and demonstrate the application of our method to obtain anti-reflection and
invisibility cloaks for a Bragg reflector.
