  The recent discovery of burst oscillations at 1122 Hz in the x-ray transient
XTE J1739-285, together with the measurement of the mass of the binary
millisecond pulsar PSR J0751+1807 (2.1 +- 0.2 solar masses) can finally allow
us to put strong, model-independent observational constraints to the equation
of state of compact stars. We show that the measurement of the moment of
inertia of PSR J0737+3039A, together with these constraints, could allow to
discriminate further the details of the inner structure of neutron stars.
Moreover, we show that if XTE J1739-285 is constituted of nucleonic matter, any
equation of state allows only a narrow range of very high masses, and this
could explain why up to now compact stars spinning faster than a millisecond
have been so difficult to detect.
