  Many hot subdwarf stars show composite spectral energy distributions
indicative of cool main sequence companions. Binary population synthesis (BPS)
models demonstrate such systems can be formed via Roche lobe overflow or common
envelope evolution but disagree on whether the resulting orbital periods will
be long (years) or short (days). Few studies have been carried out to assess
the orbital parameters of these spectroscopic composite binaries; current
observations suggest the periods are long. To help address this problem, we
selected fifteen moderately-bright (V~13) hot subdwarfs with F-K dwarf
companions and monitored their radial velocities (RVs) from January 2005 to
July 2008 using the bench-mounted Medium Resolution Spectrograph on the
Hobby-Eberly Telescope (HET). Here we describe the details of our observing,
reduction, and analysis techniques and present preliminary results for all
targets. By combining the HET data with recent observations from the Mercator
telescope, we are able to calculate precise orbital solutions for three systems
using more than 6 years of observations. We also present an up-to-date period
histogram for all known hot subdwarf binaries, which suggests those with F-K
main sequence companions tend to have orbital periods on the order of several
years. Such long periods challenge the predictions of conventional BPS models,
although a larger sample is needed for a thorough assessment of the models'
predictive success. Lastly, one of our targets has an eccentric orbit, implying
some composite-spectrum systems might have formerly been hierarchical triple
systems, in which the inner binary merged to create the hot subdwarf.
