  The outer shell of the ATLAS experiment at the LHC consists of a system of
toroidal air-core magnets in order to allow for the precise measurement of the
transverse momentum p$_T$ of muons, which in many physics channels are a
signature of interesting physics processes. For the precise determination of
the muon momentum Monitored Drift Tube chambers (MDT) with high position
accuracy are used, while for the fast identification of muon tracks chambers
with high time resolution are used, able to select muons above a predefined
p$_T$ threshold for use in the first Level of the ATLAS triggering system
(Level-1 trigger). When the luminosity of the LHC will be upgraded to 4-5 times
the present nominal value (SLHC) in about a decade from now, an improvement of
the selectivity of the ATLAS Level-1 triggering system will be mandatory in
order to cope with the maximum allowed trigger rate of 100 kHz. For the Level-1
trigger of the ATLAS muon spectrometer this means an increase of the p$_T$
threshold for single muons. Due to the limited spatial resolution of the
trigger chambers, however, the selectivity for tracks above ~20 GeV/c is
insufficient for an effective reduction of the Level-1 rate. We describe how
the track coordinates measured in the MDT precision chambers can be used to
decisively improve the selectivity for high momentum tracks. The resulting
increase in latency will also be discussed.
