  r-mode oscillations have been shown to have a significant potential to
constrain the composition of fast spinning neutron stars. Due to their high
rotation rates, millisecond pulsars (MSPs) provide a unique platform to
constrain the properties of such oscillations, if their surface temperatures
can be inferred. We present the results of our investigations of archival X-ray
data of a number of MSPs, as well as recent XMM-Newton observations of PSR
J1810+1744 and PSR J2241-5236. Using the neutron star atmosphere (NSA) model
and taking into account various uncertainties, we present new bounds on the
surface temperature of these sources. Thereby we significantly strengthen
previous bounds on the amplitude of the r-mode oscillations in millisecond
pulsars and find rigorous values as low as $\alpha\lesssim 3 \times 10^{-9}$.
This is by now about three orders of magnitude below what standard saturation
mechanisms in neutron stars could provide, which requires very strong
dissipation in the interior, strongly pointing towards a structurally complex
or exotic composition of these sources. At such low temperatures sources could
even be outside of the instability region, and taking into account the various
uncertainties we obtain for an observed surface temperature a simple frequency
bound below which r-modes are excluded in slower spinning pulsars.
