  The string-theoretic E-functions E_{str}(X;u,v) of normal complex varieties X
having at most log-terminal singularities are defined by means of
snc-resolutions. We give a direct computation of them in the case in which X is
the underlying space of the 3-dimensional A-D-E singularities by making use of
a canonical resolution process. Moreover, we compute the string-theoretic Euler
number for several compact complex threefolds with prescribed A-D-E
singularities.
