  A proposal for a novel source of isolated attosecond XUV -- soft X-ray pulses
with a well controlled carrier-envelope phase difference (CEP) is presented in
the framework of nonlinear Thomson-backscattering. Based on the analytic
solution of the Newton-Lorentz equations, the motion of a relativistic electron
is calculated explicitly, for head-on collision with an intense fs laser pulse.
By using the received formulae, the collective spectrum and the corresponding
temporal shape of the radiation emitted by a mono-energetic electron bunch can
be easily computed. For certain suitable and realistic parameters, single-cycle
isolated pulses of ca. 20 as length are predicted in the XUV -- soft X-ray
spectral range, including the 2.33-4.37 nm water window. According to our
analysis, the generated almost linearly polarized beam is extremely well
collimated around the initial velocity of the electron bunch, with considerable
intensity and with its CEP locked to that of the fs laser pulse.
