We used the 1.4 GHz NRAO VLA Sky Survey (NVSS) and 365 MHz Texas survey cat
alogs to select relatively compact (theta less than or equal to 25 ") radio
sources having exceptionally steep spectral indices alpha greater than or
equal to 1.5 (where the flux density S-nu, at frequency nu scales as S-nu p
roportional to nu(-alpha)). Our sample of 74 sources (of similar to 30,000
total sources common to both surveys) with S(365 MHz) greater than or equal
to 200 mJy in the 10 sr between delta = -35 degrees 30' and delta = 71 deg
rees 30' should be complete for spectra as steep as alpha = 3.2, but we fou
nd only four sources with alpha > 2.5. Most known sources with such steep s
pectra are pulsars (coherent radio sources), relic radio galaxies, and high
-redshift radio galaxies (synchrotron sources with spectra steepened by rad
iation losses). In fact, six of our sources have been identified with known
pulsars and one with a high-redshift (z = 3.79) radio galaxy. In order to
find possible new populations of steep-spectrum sources and classify the re
st, we made VLA images of our sources with 1 ".5 and 0 ".5 resolution at 1.
4 and 5 GHz, respectively. There are 25 doubles, 24 multicomponent sources,
16 unresolved (theta less than or similar to 0." 2) sources, and six known
pulsars. Three sources have undetermined morphologies as they were not reo
bserved with the VLA. The smallest sources have exceptionally steep spectra
for their angular sizes. New pulsars, if any, are likely to be of special
interest since they are strong but were missed by pulse-detection surveys.
Preliminary radio, infrared, and optical observations suggest that most are
high-redshift extragalactic sources.