We present fully self-consistent calculations of the thermodynamic properties of three-dimensional clean SN S Josephson junctions, where S is an s-wave short-coherence-length superconductor and N is a clean normal metal. The junction is modeled on an infinite cubic lattice such that the transverse width of the S is the same as that of the N , and its thickness is tuned from the short to long limit. Both the reduced order parameter near the SN boundary and the short coherence length depress the critical Josephson current Ic, even in short junctions. This is contrasted with recent measurements on SN S junctions finding much smaller IcRN products than expected from the standard (non-self consistent and quasiclassical) predictions. We also find unusual current-phase relations, a "phase anti-dipole" spatial distribution of the self-consistently determined contribution to the macroscopic phase, and an "unexpected" minigap in the local density of states within the N region.PACS numbers: 74.50.+r, 74.80.Fp Over the past decade, both experimental and theoretical interest in the superconductivity of inhomogeneous systems have been rekindled, thereby leading to a reexamination of even well-charted areas from the mesoscopic point of view.1 For example, the Josephson effect in a superconductor-normal-metal-superconductor (SN S) weak link was known to be the result of the macroscopic condensate wave function leaking from the S into the N region. The induction of such superconducting correlations in the N , the so-called proximity effect, has been given a new real-space interpretation through the relative phase-coherence of quasiparticles, correlated by Andreev reflection at the SN interface.2 Moreover, the realization of the importance of tracking the phase-coherence of single particle wave-functions in proximity-coupled metals of mesoscopic size has also unearthed new phenomena, such as quantization of the critical current in ballistic mesoscopic short SN S junctions at low enough temperature.3,4 In short clean junctions, as T → 0, the critical supercurrent I c = e∆/ carried by a single conducting channel depends only on the superconducting energy gap ∆ as the smallest energy scale ∆ < E Th = v N F /L (in the long junction limit I c ∼ E Th is set 5 by the "ballistic" Thouless energy E Th < ∆, which is a single quasiparticle property determined by the Fermi velocity v N F in the N interlayer of length L). Thus, both mesoscopic and "classical" clean point-contact SN S junctions, with ballistic transport ℓ > L (ℓ is the mean free path), are predicted to exhibit the same I c R N = π∆/e product at T = 0. This has been known for quite some time as the KulikOmelyanchuk (KO) formula, 6 where R N is the Sharvin point contact resistance R N = h/2e 2 M of the ballistic N region containing M conducting channels.Recent experimental activity 7 on highly transparent 8 ballistic short SN S junctions, where both I c and R N are independent of the junction length, reveals much lower values of I c R N than the KO formula (similarly, the cri...