  Recent measurements of the cosmic ray (CR) antiproton flux have been shown to
challenge existing CR propagation models. It was shown that the reacceleration
models designed to match secondary to primary nuclei ratios (e.g., B/C) produce
too few antiprotons. In the present paper we discuss one possibility to
overcome these difficulties. Using the measured antiproton flux AND B/C ratio
to fix the diffusion coefficient, we show that the spectra of primary nuclei as
measured in the heliosphere may contain a fresh local "unprocessed" component
at low energies perhaps associated with the Local Bubble, thus decreasing the
measured secondary to primary nuclei ratio. The independent evidence for SN
activity in the solar vicinity in the last few Myr supports this idea. The
model reproduces antiprotons, B/C ratio, and elemental abundances up to Ni
(Z<=28). Calculated isotopic distributions of Be and B are in perfect agreement
with CR data. The abundances of three "radioactive clock" isotopes in CR, 10Be,
26Al, 36Cl, are all consistent and indicate a halo size z_h~4 kpc based on the
most accurate data taken by the ACE spacecraft.
