  Hadronic tau decay data is used to study the reliability of various finite
energy sum rules (FESR's). For intermediate scales (of order 2-3 GeV^2), those
FESR's with weights s^k are found to have significant errors, whereas those
with weights having a zero at the juncture (s=s_0) of the cut and circular part
of the contour work very well. It is also shown that a combination of two such
sum rules allows rather strong constraints to be placed on the hadronic
spectral function without sacrificing the excellent agreement between OPE and
hadronic representations. The method then is applied to the strangeness -1 and
pseudoscalar isovector channels, where it is shown to provide novel constraints
on those ansatze for the unmeasured continuum parts of the spectral functions
employed in existing extractions of m_u+m_d, m_s. The continuum ans\"atz in the
latter channel, in particular, is shown to produce a rather poor match to the
corresponding OPE representation, hence re-opening the question of the value of
the light quark mass combination m_u+m_d.
