  The fourth transient accreting millisecond pulsar XTE J1807-294 was observed
during its February/March 2003 outburst by INTEGRAL, partly simultaneously with
the XMM-Newton and RXTE satellites. We present here the first study of the
0.5-200 keV broad-band spectra of the source. On February 28, the source
spectrum was consistent with thermal Comptonization by electrons of temperature
\~40 keV, considerably larger than the value (~10 keV) previously derived from
the low energy XMM-Newton data alone. The source is detected by INTEGRAL up to
200 keV with a luminosity in the energy band (0.1-200) keV of 1.3 x 10E37 erg/s
(assuming a distance of 8 kpc). 22 days later the luminosity dropped to 3.6 x
10E36 erg/s. A re-analysis of XMM-Newton data yields the orbital Doppler
variations of the pulse period and refines the previous ephemeris. For this
source having shortest orbital period of any known binary radio or X-ray
millisecond pulsar, we constrain the companion mass Mc < 0.022 Msun, assuming
minimum mass transfer driven by gravitational radiation. Only evolved dwarfs
with a C/O composition are consistent with the Roche lobe and gravitational
radiation constraints, while He dwarfs require an unlikely low inclination.
